Coherent optical channel substitution

ABSTRACT

In an optical data transmission system, one channel is removed from a group of wavelength division multiplexed optical channels and another channel carrying different information at the same wavelength is inserted in its place. The process occurs by adding an optical signal whose electric field is the difference between the electric field of the new and old channels. The difference calculation takes into account the phase of the incoming WDM channel and phase of the laser source of the difference signal. The method has applications in optical transmission networks as add-drop nodes and optical regenerators, for generation of high bandwidth optical signals, and for secret optical communications.

RELATED APPLICATIONS

This application is a divisional application of a U.S. patentapplication (Ser. No. 11/377,783) entitled “COHERENT OPTICAL CHANNELSUBSTITUTION” filed Mar. 16, 2006 by Michael G. Taylor now U.S. Pat. No.7,742,701 which claims the benefit of U.S. Provisional PatentApplication Ser. No. 60/662,607 by Michael G. Taylor, filed Mar. 16,2005, and is hereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to optical data transmission over optical fibers.Specifically, and not by way of limitation, the present inventionrelates to optical data transmission utilizing coherent optical channelsubstitution.

2. Description of the Related Art

Information has been transmitted over optical fibers for some time.Details about this field are disclosed in “Optical CommunicationSystems,” by J. Gowar (Prentice Hall, 2nd ed., 1993) and “Fiber-opticcommunication systems” by G. P. Agrawal (Wiley, 2nd ed., 1997), whichare herein incorporated by reference. The information is usually in theform of binary digital signals, i.e. logical “1”s and “0”s, but fiberoptics is also used to transport analog signals, such as cable TVsignals. The present invention may be utilized with either digital oranalog signals. However, for simplicity and exemplary purposes only,digital signals are discussed with the present invention. It should beunderstood by those skilled in the art that the present invention mayalso be used with analog signals. Every optical data transmission systemhas a transmitter, which emits light modulated with information into thefiber, and a receiver at the far end which detects the light andrecovers the information. A long distance digital link may also use oneor more digital regenerators at intermediate locations. A digitalregenerator receives a noisy version of the optical signal, makesdecisions as to what sequence of logical values (“1”s and “0”s) wastransmitted, and then transmits a clean noise-free signal containingthat information forward towards the destination.

As discussed, in Agrawal, an optical signal that is modulated has abroadened spectrum occupying a range of frequencies. Considerpropagation of Gaussian input pulses in optical fibers having theamplitude

${A(t)} = {A_{0}{\exp\left( {{- \frac{1 + {{\mathbb{i}}\; C}}{2}}\left( \frac{t}{T_{0}} \right)^{2}} \right)}}$where A₀ is the peak amplitude. The parameter T₀ represents thehalf-width at 1/e-intensity point. The parameter C governs the linearfrequency chirp imposed on the pulse. A pulse is said to be chirped ifits carrier frequency changes with time. The Fourier spectrum of achirped pulse is broader than that of the unchirped pulse. This can beseen by taking the Fourier transform of the equation above for A(t), sothat

${\overset{\sim}{A}(\omega)} = {{A_{0}\left( \frac{2\pi\; T_{0}^{2}}{1 + {{\mathbb{i}}\; C}} \right)}^{1/2}{\exp\left( {- \frac{\omega^{2}T_{0}^{2}}{2\left( {1 + {{\mathbb{i}}\; C}} \right)}} \right)}}$The spectral half-width (at 1/e-intensity point) is given byΔω₀=(1+C ²)^(1/2) T ₀ ⁻¹In the absence of frequency chirp (C=0), the spectral width satisfiesthe relation Δω₀T₀=1.

As described herein, if an optical signal is said to carry informationthen that information is useful to a recipient of the optical signal.However, there are other disclosures which employ a broader definition,where any optical signal that varies with time is said to carryinformation. The broader definition does not apply in the explanation ofthe present invention. The variations of the optical signal with timemust convey a message that is of value to a recipient in order for theoptical signal to contain information.

In the 1990's optical amplifiers were deployed in telephony and cable TVnetworks, in particular erbium doped fiber amplifiers (EDFAs) weredeployed. These devices amplify the optical signals passing throughthem, and overcome the loss of the fiber without the need to detect andretransmit the signals. A typical long distance fiber optic digital linkmight contain some digital regenerators between the information sourceand destination, with several EDFAs in between each pair of digitalregenerators.

A. WDM Network Topologies and Add-Drop

Also in the 1990's, wavelength division multiplexing (WDM) wascommercially deployed, which increased the information carrying capacityof the fiber by transmitting several different wavelengths in parallel.

There are several different topologies that may be employed in a WDMfiber optic network, which are illustrated in FIGS. 1 a through e. Thedashed, dotted and solid lines in FIGS. 1 a through e represent threedifferent wavelengths. The simplest topology is point-to-pointtransmission, shown in FIG. 1 a, where all the wavelengths originate inthe same location A (101) and terminate together at another location B.As shown in FIG. 1 b, broadcast topologies are possible where a signalfrom one transmitter is split and goes to more than one receiver(locations B (102) and C (103) in FIG. 1 b). In a WDM transmissionsystem, one WDM channel can be dropped at an intermediate site while theothers continue, as shown in FIG. 1 c. The dropped channel 104 may bedetected at that intermediate site (node D (105) in FIG. 1 c).Alternatively, as shown in FIG. 1 d, the dropped channel may traversemore fiber spans (from D (105) to E (106)) before being detected. Theprocess of add-drop, illustrated in FIG. 1 e, means that as well asdropping a WDM channel 104 of a certain wavelength at an intermediatesite 107, a channel 108 of the same wavelength carrying new content isinserted and continues with the other channels. The added and droppedchannels may originate and terminate at the add-drop node, as is shownin FIG. 1 c or they may originate and terminate at a remote locationfrom the add-drop node, in analogy with FIG. 1 d. To make an add-dropnode (node D (105) in FIG. 1 e), it is necessary to block light comingfrom the transmitter at A at the add-drop wavelength so it does notcontinue to B, and pass all other wavelengths going from A to B. U.S.Pat. No. 5,748,349 gives an example of the apparatus to perform theadd-drop function. A high extinction is required for the blockingoperation because the crosstalk onto the channel added at location D isin-band crosstalk, which causes more degradation to a signal thanout-of-band crosstalk. Except for the broadcast case, fiber optic linksare typically bidirectional and symmetric, so another channel, often inanother fiber, is transmitted from the receiver site to the transmittersite.

Most fiber optic transmission systems installed today have staticadd-drop configurations. There has been substantial research intoall-optical networks where connections between nodes are set up andtaken down in an automated fashion according to demand. All-opticalnetworks are described in “A Precompetitive Consortium on Wide-BandAll-Optical Networks,” by S. B. Alexander et al. (IEEE J. LightwaveTechnol., vol. 11, no. 5/6, p. 714-735, 1993) which is incorporatedherein by reference. The add-drop technology must be able to switchmultiple wavelength channels from add-drop to passthrough. Also thecomponents involved in signal transmission, that is transmitters andreceivers, fiber spans, optical amplifiers, etc., must be able tosupport a wide range of possible end-to-end link scenarios, as theconnections in an all-optical network are changed according to customerdemand. Using the add-drop technology to switch in a digital regeneratorat intervals along the link helps support long transmission distancescenarios. Hence, there is a need for a flexible add-drop technologythat may be switched in and out at any one wavelength and which may beoperated at a range of wavelengths. Also there is a need for a digitalregenerator which may be switched in and out of a link and which may beoperated at a range of wavelengths.

B. Direct Detection & Coherent Detection

The transmitter unit for a single WDM channel contains a light source,usually a single longitudinal mode semiconductor laser. Information isimposed on the light by direct modulation of the laser current, or byexternal modulation, that is by applying a voltage to a modulatorcomponent that follows the laser. The receiver employs a photodetector,which converts light into an electric current. There are two ways ofdetecting the light: direct detection and coherent detection. All theinstalled transmission systems today use direct detection. Although itis more complex, coherent detection has some advantages, and it washeavily researched into in the 1980s and the start of the 1990s, and hasbecome of interest once again in the past few years.

Most deployed transmission systems impose information on the amplitude(or intensity, or power) of the signal. The light is switched on totransmit a “1” and off to transmit a “0”. In the case of directdetection, the photodetector is presented with the on-off modulatedlight, and consequently the current flowing through it is a replica ofthe optical power. After amplification the electrical signal is passedto a decision circuit, which compares it to a reference value. Thedecision circuit outputs an unambiguous “1” or “0”.

There is another class of modulation formats where information isencoded on the phase of the optical signal, such as optical differentialphase shift keying (oDPSK). A photodetector does not respond to changesin the phase of the light falling on it, so a passive component called adiscriminator is used before the photodetector receives the opticalsignal. The discriminator converts the changes in phase into changes inpower to which the photodetector can respond.

Since a photodetector does not respond to the phase portion of anoptical wave, if two wavelengths are input to the photodetector, thephotodetector does not distinguish between them. The photocurrent isproportional to the sum of the powers of the two wavelength channels.WDM systems work by using passive optical filter components to separateout the different wavelength channels at the receive terminal, so eachphotodetector sees only one channel. This approach puts a limit on howclose the channels can be spaced, which comes from the optical filter'sability to pass one channel and reject its neighbours.

The coherent detection method treats the optical wave more like radio,inherently selecting one wavelength and responding to its amplitude andphase. “Fiber-optic communication systems” by G. P. Agrawal provides anintroduction to coherent detection. Coherent detection involves mixingthe incoming optical signal with light from a local oscillator (LO)laser source. FIG. 2 illustrates an example of a coherent receiversuitable for detecting a binary phase shift keyed (BPSK) signal. Theincoming signal 201 is combined with light 202 from a continuous wave(c.w.) local oscillator in a passive 2:1 combiner 203. The LO light hasclose to the same state of polarisation (SOP) as the incoming signal andeither exactly the same wavelength (homodyne detection) or a nearbywavelength (heterodyne detection). When the combined signals aredetected at photodetector 204, the photocurrent contains a component ata frequency which is the difference between the signal and localoscillator optical frequencies. This difference frequency component,known as the intermediate frequency (IF), contains all the information,that is amplitude and phase, that was on the optical signal. Because thenew carrier frequency is much lower, typically a few gigahertz insteadof 200 THz, all information on the signal can be recovered usingstandard radio demodulation methods. Coherent receivers see only signalsclose in wavelength to the local oscillator, and so by tuning the LOwavelength, a coherent receiver can behave as though having a built-intunable filter. When homodyne detection is used, the photocurrent is areplica of the information and can be passed to the decision circuit 206which outputs unambiguous “1” or “0” values. With heterodyne detection,the photocurrent must be processed by a demodulator 205 to recover theinformation from the IF. FIG. 2 illustrates a configuration forsingle-ended detection. There are other configurations for coherentdetection. For example, a balanced detection configuration is obtainedby replacing the 2:1 combiner by a 2:2 combiner, each of whose outputsare detected and the difference taken by a subtracting component.

Following is a mathematical description of the coherent detectionprocess. (The complex notation for sinusoids is summarised in theAppendix.) The electric field of the signal may be written asRe└E_(s)(t)e^(iω) ^(s) ^(t+iφ) ^(s) ^((t))┘where E_(s) (t) is the slowly varying envelope containing theinformation encoded on amplitude and phase of the optical signal, ω_(s)is the angular frequency of the optical carrier, and φ_(s) (t) is theslowly varying phase noise associated with the finite linewidth of thelaser. Writing the phase noise separate from the modulation envelopeE_(s) (t) has the advantage that in the case of digital informationtransmission E_(s) (t) takes on only a small number of possible values,depending on the digital signal format. Similarly, the electric field ofthe local oscillator is written asRe└E_(LO)e^(iω) ^(LO) ^(t+iφ) ^(LO) ^((t))┘where E_(LO) is a constant given that the local oscillator is c.w.,ω_(LO) is the angular frequency of the LO, and φ_(LO) (t) is the phagenoise on the LO. The electric fields of the signal and LO are written asscalar quantities because it is assumed that they have the same state ofpolarisation. The electric field of the light arriving at thephotodetector in FIG. 2 is the sum of the two electric fieldsE ₁ =Re└E _(s)(t)e ^(i(ω) ^(s) ^(t+φ) ^(s) ^((t))) +E _(LO) e ^(i(ω)^(LO) ^(t+φ) ^(LO) ^((t)))┘and the optical power isP ₁ =E ₁ *E ₁P ₁ =|E _(s)(t)|² +|E _(LO)|²+2Re[E _(s)(t)E _(LO) *e ^(i(ω) ^(s) ^(−ω)^(LO) ^()t+i(φ) ^(s) ^((t)−φ) ^(LO) ^((t)))]  (1)In the case of single ended detection only one output of the combiner isused. |E_(LO)|² is constant with time. |E_(s) (t)|² small given that thelocal oscillator power is much larger than the signal power, and forphase shift keying (PSK) and frequency shift keying (FSK) modulationformats |E_(s) (t)|² is constant with time. The dominant term inequation 1 is the beat term Re└E_(s) (t)E_(LO)*e^((iω) ^(s) ^(−ω) ^(LO)^()t+i(φ) ^(s) ^((t)−φ) ^(LO) ^((t)))┘. In appropriate conditions thebeat term can be readily obtained from the photocurrent in thesingle-ended detection case. Alternatively when |E_(s) (t)|² is notsmall and varies with time, the beat term is produced directly by thebalanced detection configuration. The equations that follow refer to thebeat term. It is assumed that this term is obtained by single endeddetection assuming the other terms do not contribute or by balanceddetection.

There are two modes of coherent detection: homodyne and heterodyne. Inthe case of homodyne detection the frequency difference between signaland local oscillator is zero, and the local oscillator laser has to bephase locked to the incoming signal in order to achieve this. Forhomodyne detection the term e^(i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ) ^(s)^((t)−φ) ^(LO) ^((t))) is 1, and the beat term becomesRe└E_(s)(t)E_(LO)*┘For the binary phase shift keying (BPSK) modulation format for example,E_(s)(t) takes on the value 1 or −1 depending on whether a logical “1”or “0” was transmitted, and the decision circuit can simply act on thebeat term directly.

With heterodyne detection there is a finite difference in opticalfrequency between the signal and local oscillator. All the amplitude andphase information on the signal appears on a carrier at angularfrequency (ω_(s)−ω_(LO)), the intermediate frequency, and it can bedetected with a demodulator using standard radio detection methods, suchas synchronous detection, envelope detection or differential detection.Typically homodyne detection gives better performance than heterodynedetection, but is harder to implement because of the need for phaselocking.

C. Sampled Coherent Detection

A new method of coherent detection called sampled coherent detection hasbeen proposed and demonstrated recently, as described in U.S. PatentApplication No. 2004/0114939 and in “Coherent detection method using DSPfor demodulation of signal and subsequent equalization of propagationimpairments” by M. G. Taylor (IEEE Phot. Tech. Lett., vol. 16, no. 2, p.674-676, 2004) which are herein incorporated by reference. Digitalsignal processing (DSP) is employed in this method to obtain theinformation carried by a signal from the beat products seen at theoutputs of a phase diverse hybrid. The field of digital signalprocessing is summarized below.

In sampled coherent detection, the signal and local oscillator arecombined in a passive component called a phase and polarisation diversehybrid. FIG. 3 shows a sampled coherent detection apparatus. The fouroutputs of the phase and polarisation diverse hybrid are detected byseparate photodetectors 312 and then, after optional amplification byamplifiers 313, they are sampled by A/D converters 314. The samplevalues of the A/D converters are processed by the digital signalprocessor 315 to calculate the complex envelope of the signal electricfield over time. The phase and polarisation diverse hybrid has fouroutputs 308 through 311 in the example of FIG. 3, where single endeddetection is used. The top two outputs 308 and 309 have the LO in onestate of polarisation, e.g., the horizontal polarisation, and the lowertwo outputs 310 and 311 have the LO in the orthogonal, vertical,polarisation. For each of the two LO polarisation states, the signal iscombined with the LO in a 90° hybrid 305, also known as a phase diversehybrid. The phase of the LO relative to the signal in one output of the90° hybrid is different by π/2 radians (i.e. 90°) compared to the phaseof the LO relative to the signal in the other output. This phase shiftcan be implemented by extra path length in one arm 306 of the 90° hybridcarrying the LO compared to the other arm 305, as can be seen in FIG. 3.The orthogonal SOP relationship between the two 90° hybrids is achievedby using a polarization beamsplitter 304 to divide light from the localoscillator 302 between the two hybrids and a standard 1:2 splitter 303to divide the incoming signal light 301.

The following mathematical treatment explains how the electric field ofthe signal is obtained from the outputs of the phase and polarisationdiverse hybrid. The incoming signal electric field can be written asRe└E_(s)(t)e^(iω) ^(s) ^(t+iφ) ^(s) ^((t)┘)where E_(s) (t) is a Jones vector, a two-element vector comprising thepolarisation components of the electric field in the horizontal andvertical directions. The use of Jones vectors is summarised in theAppendix.

${E_{s}(t)} = \begin{pmatrix}{E_{sx}(t)} \\{E_{sy}(t)}\end{pmatrix}$Each of the four outputs of the phase and polarization diverse hybrid inFIG. 3 contains signal Re└E_(s) (t) e^(iω) ^(s) ^(t+iφ) ^(s) ^((t))┘.The local oscillator in the four outputs is different, and can bewritten as followstop output . . . Re└E_(LO)e^(iω) ^(LO) ^(t+iφ) ^(LO) ^((t)){circumflexover (x)}┘2nd output . . . Re└iE_(LO)e^(iω) ^(LO) ^(t+iφ) ^(LO) ^((t)){circumflexover (x)}┘3rd output . . . Re└E_(LO)e^(iω) ^(LO) ^(t+iφ) ^(LO) ^((t))ŷ┘4th output . . . Re└iE_(LO)e^(iω) ^(LO) ^(t+iφ) ^(LO) ^((t))ŷ┘In the top two arms the LO is horizontally polarized, in the directionof Jones unit vector {circumflex over (x)}, and in the lower two armsvertical in the direction of ŷ. The π/2 phase shift is accounted for bythe multiplicative imaginary number i. The beat term parts of theoptical powers in the four outputs 308 through 311 are thereforebeat term 1=Re└E _(sx)(t)E _(LO) *e ^(i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ)^(s) ^((t)−φ) ^(LO) ^((t)))┘beat term 2=Im└E _(sx)(t)E _(LO) *e ^(i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ)^(s) ^((t)−φ) ^(LO) ^((t)))┘beat term 3=Re└E _(sy)(t)E _(LO) *e ^(i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ)^(s) ^((t)−φ) ^(LO) ^((t)))┘beat term 4=Im└E _(sy)(t)E _(LO) *e ^(i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ)^(s) ^((t)−φ) ^(LO) ^((t)))┘So the envelope of the signal electric field can be calculated from

$\begin{matrix}{{E_{s}(t)} = {\frac{{\mathbb{e}}^{{{- {{\mathbb{i}}{({\omega_{s} - \omega_{LO}})}}}t} - {{\mathbb{i}}{({{\phi_{s}{(t)}} - {\phi_{LO}{(t)}}})}}}}{E_{LO}^{*}}\begin{pmatrix}{\left( {{beat}\mspace{14mu}{term}\mspace{14mu} 1} \right) + {{\mathbb{i}}\left( {{beat}\mspace{14mu}{term}\mspace{14mu} 2} \right)}} \\{\left( {{beat}\mspace{14mu}{term}\mspace{14mu} 3} \right) + {{\mathbb{i}}\left( {{beat}\mspace{14mu}{term}\mspace{14mu} 4} \right)}}\end{pmatrix}}} & (2)\end{matrix}$To implement equation 2 in the digital signal processor, the frequencydifference ω_(s)−ω_(LO) and phase difference φ_(s) (t)−φ_(LO) (t) mustbe known. These parameters can be obtained using a standard phaseestimation technique, such as described in “Digital Communications” byJ. G. Proakis (McGraw-Hill, 4th ed., 2000) and “Digital communicationreceivers: synchronization, channel estimation & signal processing” byH. Meyr, M. Moeneclaey & S. A. Fechtel (Wiley, 1998).

Transmission over a length of optical fiber transforms the state ofpolarization of an optical signal, so that the digital values taken onby E_(s) (t) as seen at the receive end of a fiber optic transmissionsystem are typically not the same as those imposed at the transmit end.The polarization transformation can be reversed within the DSP byapplying the appropriate rotation Jones matrix. The correct rotationmatrix can be found by exploring the available space and then locking onto the matrix which gives the best quality signal. The polarizationtransformation of the optical fiber typically changes slowly, so therotation matrix must be allowed to update.

The Jones vector E_(s) (t) constitutes a complete description of theoptical signal, or more precisely of the signal's optical spectrum inthe region of the local oscillator. This means that any parameter of theoptical signal can be deduced from E_(s) (t). Employing sampled coherentdetection is more complex than direct detection, but has many benefits.Phase encoded modulation formats can be employed, such as BPSK andquadrature phase shift keying (QPSK), which offer better sensitivitythan on-off modulation formats. Also polarization multiplexed formatscan be employed, which offer twice the information capacity for a givenbandwidth of electro-optic components and a given optical spectralbandwidth. The polarization demultiplexing operation is performed withinthe digital signal processor, so no additional optical components areneeded for it. In a long fiber optic transmission system carrying highbit rate signals the optical fiber propagation effects, such aschromatic dispersion and polarization mode dispersion, distort thesignals. With sampled coherent detection the propagation effects can bereversed within the DSP by applying an appropriate mathematicaloperation.

Finally, a key benefit of sampled coherent detection is that it isequivalent to passing the signal through a narrow optical filtercentered on the local oscillator wavelength, so no narrow optical filtercomponents are needed for WDM. The LO can be tuned in wavelength, whichis equivalent to tuning the optical filter, and lower WDM channelspacings should be possible with sampled coherent detection than withany WDM implementation using passive optical filters. However, becausesampled coherent detection is a means of observing a signal, the narrowchannel spacing is not available in conjunction with a WDM channeladd-drop. At the add-drop node the dropped channel must be extinguishedbefore the add channel is inserted, and even if the narrowest availablephysical optical filter were used, it would work correctly only if theneighboring channels were spaced farther away than if the onlyconstraint were the ability to detect with sampled coherent detection.Hence it is desirable to have a method of dropping and adding a WDMchannel which allows the same low channel spacing as with detectiononly.

D. Digital Signal Processing

The present invention utilizes digital signal processing (DSP). DSP isdescribed in “Understanding Digital Signal Processing” by R. G. Lyons(Prentice Hall, 1996), herein incorporated by reference. A signalprocessor is a unit which takes in a signal, typically a voltage vs.time, and performs a predictable transformation on it, which can bedescribed by a mathematical function. FIG. 4 a shows a generic analogsignal processor (ASP). The box 402 transforms the input signal voltage401 into the output signal voltage 403, and may contain a circuit ofcapacitors, resistors, inductors, transistors, etc. FIG. 4 b illustratesa digital signal processor. First, the input signal 401 is digitized bythe analog to digital (A/D) converter 404, that is converted into asequence of numbers, each number representing a discrete time sample.The core processor 406 uses the input numerical values to compute therequired output numerical values, according to a mathematical formulathat produces the required signal processing behavior. The output valuesare then converted into a continuous voltage vs. time by the digital toanalog (D/A) converter 408. The connections 405 and 407 between the A/Dand D/A converters and the core processor are typically implemented asparallel data connections, which is why they are drawn as grey strips inFIG. 4 b as well as in some of the other figures.

Digital signal processing can be a better solution than analog signalprocessing for a task because the signal processing operation can bevaried under programmable control and because operations can beperformed that would require too much complexity if done by ASP. Theexamples presented herein refer to a single digital signal processor,but in fact the DSP may be made up of several processors thatcommunicate with one another, and they do not have to be co-located.

E. Secret Communications

Additionally, there are applications for secret communications, wherethe information being transmitted is not available to someone who hasaccess to the transmission system at an intermediate location. Opticaltransmission is not inherently secure. An eavesdropper who taps off someof the optical signal power may observe the same signal as the intendedrecipient. If the signal is a digital signal the eavesdropper canreconstruct the same digital sequence as the intended recipient. Using aphase or polarization encoded format will stop the eavesdropperreceiving the information if direct detection is utilized, but not ifcoherent detection also is used.

Many encryption methods are available that operate on the digital data,as discussed in “Applied cryptography” by B. Schreier (Wiley, 2nd ed.,1996). Clearly, one of these encryption methods could be used prior tooptical transmission and the corresponding decryption method afterdetection, to make the optical transmission link secure. Most encryptionmethods employ a secret key known to the intended recipient, but not toan eavesdropper. The key is a piece of data typically shorter than themessage it encodes. The security of the code is maintained even if theeavesdropper knows the design of the code, provided he does not know thekey being used by that particular recipient. If the length of the key ism bits, then the eavesdropper can break the code by trying all 2^(m)possible values of key. m is chosen as a large value such that anexhaustive key search would require an unreasonable amount of time andeffort. However, for many codes whose design has been published a modeof decrypting the code has been found, often after years of research,which requires less effort than trying 2^(m) key combinations. Thus itis desirable to find new encrypting methods which inherently require anunfeasibly long time and/or large resources to break.

Transmission in the optical domain offers some features which allowencryption with a higher level of security than using the data domain.For example, the optical domain has a much higher information carryingcapacity than an electrical cable or link. Frequency hopping (FH) is amethod that has been used for some time in secure radio transmission,and can be applied to the optical domain as described in “Secure opticalcommunications utilizing PSK modulation, polarization multiplexing andcoherent homodyne detection with wavelength and polarization agility,”by A. Salamon et al. (Military Communications Conference 2003 (MILCOM2003), vol. 1, p. 274-282, 2003). The optical carrier frequency ω_(s) ischanged suddenly over time according to a frequency hop plan derivedfrom the secret key. The intended recipient who knows the frequency hopplan can tune his receiver to the correct channel ω_(s) (t) as itchanges with time, and recover the signal that was sent. An eavesdroppermust listen to all possible channels to be able to assemble the signalcorrectly. Security is improved by frequency hopping, but it can bedefeated by an eavesdropper who has equipment to listen to all channels.

Thus, there is a need for an optical domain encryption method which canbe implemented cost effectively for the intended information recipientbut which is unfeasible to overcome by an eavesdropper.

SUMMARY OF THE INVENTION

The invention disclosed here is a method and apparatus to remove a WDMchannel from an optical fiber and replace it with another channel of thesame wavelength carrying different information. The substitution of theWDM channel is achieved by combining with the light passing through theoptical fiber a modulated beam of light whose electric field can beconsidered to be the sum of two components. The first component cancelsthe WDM channel that is to be removed by destructive interference. Thesecond component corresponds to the new WDM channel containing the newdifferent information. The modulation on the beam of light that is addedtakes into account the optical phase of the WDM channel to be removedcompared to the phase of the laser source from which the beam isobtained. Also, the modulation on the light beam takes into account therelative states of polarization of the WDM channel to be removed and theadd laser source.

In one aspect, the present invention performs an add-drop function in anfiber optic telecommunications network.

In another aspect, the invention acts as a digital regenerator whichreplaces a noisy WDM channel with a channel at the same wavelength thathas no noise. The density of WDM channels may be so high thatdemultiplexing using passive optical components is not possible.

In another aspect, the invention is a method to synthesize a WDM channelthat occupies a wide optical bandwidth, such as a high baud rate digitalsignal, using several lasers at neighboring wavelengths. Each laser ismodulated at a slower rate than would be required to generate the highbaud rate optical signal directly.

In yet another aspect, the invention provides a way to phase lock onelaser to an incoming optical signal without using feedback.

In a further aspect, the present invention is a secret communicationsystem. Information which is intended to be secret is inserted into thespectrum of a broadband optical noise source, in such a way that aneavesdropper cannot identify the true information-bearing channel apartfrom a slice of noise spectrum. The information may be coded beforebeing modulated onto an optical carrier in such a way that the opticalsignal resembles a spectral slice of optical noise. Only the intendedrecipient, who knows the spectral location of the channel and the codingmethod used to disguise the channel, can obtain the information on thechannel without unreasonable time and effort.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 (Prior Art) illustrates five different WDM network topologies(point-to-point, broadcast, drop node, drop node with spur, and add-dropnode) with dashed, dotted and solid lines representing three differentwavelengths;

FIG. 2 (Prior Art) illustrates a coherent receiver;

FIG. 3 (Prior Art) illustrates a polarization and phase diverseconfiguration for sampled coherent detection;

FIG. 4 (Prior Art) illustrates generic diagrams of an analog signalprocessor and a digital signal processor;

FIG. 5 illustrates a basic coherent channel substitution apparatus;

FIG. 6 illustrates an add laser followed by a modulation subsystem;

FIG. 7 illustrates input and output monitors fitting in a coherentchannel substitution system;

FIG. 8 illustrates an add laser with modulation subsystem for a simplemodulation format case;

FIG. 9 illustrates a coherent channel substitution system using an addlaser in a phase locked loop;

FIG. 10 provides an example of spectral occupancy of 3 input channels, 4add channels and 2 output channels, in relation to the multiple WDMchannel architecture of coherent channel substitution;

FIG. 11 illustrates an apparatus for coherent channel substitution usingmultiple add lasers;

FIG. 12 illustrates a simple configuration for add laser phasecomparison unit;

FIG. 13 illustrates an alternative embodiment of a multiple channelcoherent channel substitution configuration;

FIG. 14 illustrates possible stitching functions for the low opticalfrequency channel, intermediate channels, and the high optical frequencychannel;

FIG. 15 illustrates an apparatus to achieve optical phase locking;

FIG. 16 illustrates a configuration to synthesize a high bandwidthsignal from multiple modulated laser sources;

FIG. 17 illustrates the notch in the spectrum of broadband optical noise(solid line) carved by coherent channel substitution, together with thespectrum of the corresponding inserted signal (dashed line); and

FIG. 18 illustrates the spectrum of a signal embedded in broadband noisewhere the shape of the signal does not match the notch carved in thenoise, as seen for two different observation times.

DESCRIPTION OF THE INVENTION

FIG. 5 illustrates the most basic implementation of coherent channelsubstitution. The present invention adds to the fiber a modulated signal503 from the add laser which is the difference between the actual signalof the WDM channel at the add laser's wavelength arriving at the inputand the desired output WDM channel signal. This converts the inputsignal 501 into the desired output signal 504. The field modulated ontothe add laser 505 must take into account the phase noise on the addlaser and on the input signal, as well as their respective SOPs. Themodulation to the add laser is applied by a modulator 506 and a combiner502 introduces the modulated add signal 503 into the main fiber. Themodulator is controlled by several analog voltages which are set by D/Aconverters 508 which are, in turn, set by the digital signal processor507. The DSP may also control the add laser directly, which is indicatedby the dotted line in FIG. 5.

The feature that is central to the configuration of FIG. 5 is thecombining of one optical signal 501 with another optical signal 503.There are many examples in the prior art where two optical signals arecombined. The present invention is different from the prior art examplesin that the two signals purposely coherently interfere to form a newoptical signal whose electric field envelope is the desired electricfield envelope. Two optical signals coherently interfere only if theiroptical spectra substantially overlap, if the second optical signal hassubstantial content in the state of polarization of the first opticalsignal, and if the two optical signals are present at the same time. Inone prior art example, wavelength division multiplexing, the two opticalsignals are two different wavelength channels being combined. Thepresent invention is different from the WDM case in that the inputsignal 501 and add signal 503 substantially overlap in optical spectrum.Another prior art example is polarization multiplexing of two opticalsignals, where the two signals to be combined have mutually orthogonalstates of polarization. The present invention is different from thepolarization multiplexing case in that the input signal 501 hassubstantial content having the same SOP as the add signal 503. Anotherprior art example is in optical packet transmission, where two bursts oflight are combined that are on at different times. Again the presentinvention is different from this optical packet transmission casebecause the input signal 501 and add signal 503 substantially overlap intime of presence. In these prior art examples there is sometimes apartial overlap of the optical spectrum or the states of polarization ofthe two optical signal being combined, and the degree of overlap is keptlow in order for the system to function correctly. In the case of thepresent invention, the overlap of the optical spectrum, SOP and time ofpresence of the two optical signals being combined is intentional. Thus,the system would not function correctly if the overlap were avoided.

The process of changing the input optical signal into the output signalis described mathematically as follows. The input optical fiber containsa signal with electric field Re└E_(in) (t) e^(iω) ^(in) ^(t+iφ) ^(in)^((t))┘, and perhaps other WDM channels in addition. This is theelectric field that would be observed at point A in FIG. 5 if the addlaser were switched off. It is desired to substitute this signal withanother having the same nominal wavelength, whose electric field isRe└E_(out) (t) e^(iω) ^(out) ^(t+iφ) ^(out) ^((t))┘ (referenced at pointA). Here ω_(out) and φ_(out) (t) are stated explicitly, although forsome applications, it may be simplest to keep them the same as ω_(in)and ω_(in) (t). The change in channel may be achieved by adding a signalto the optical fiber whose electric field isRe└E_(out)(t)e^(iω) ^(out) ^(t+iφ) ^(out) ^((t))−E_(in)(t)e^(iω) ^(in)^(t+iφ) ^(in) ^((t))┘The add laser has an electric field, before modulation is applied to it,of Re└E_(add) e^(iω) ^(add) ^(t+iφ) ^(add) ^((t)){circumflex over(p)}_(add)┘, as would be observed at point B in FIG. 5. Thus, theoptical spectrum of the add optical signal has a substantially similarshape to the optical spectrum of the input optical signal. E_(add) isconstant given that the laser is c.w., and {circumflex over (p)}_(add)is the Jones unit vector of the add laser's SOP. (The principle ofcoherent channel substitution can be applied even if the add laser hasmodulation on it by following the equations below with a time dependentE_(add){circumflex over (p)}_(add).) When a signal is represented as aJones vector, the act of modulating the signal is expressedmathematically as premultiplication by a time-dependent Jones matrix. Toachieve the desired coherent substitution function, the add laser mustbe modulated by Jones matrix M_(add) (t) such that

$\begin{matrix}{{{{M_{add}(t)}E_{add}{\mathbb{e}}^{{{\mathbb{i}\omega}_{add}t} + {{\mathbb{i}\phi}_{add}{(t)}}}{\hat{p}}_{add}L_{BA}} = {{{E_{out}(t)}{\mathbb{e}}^{{{\mathbb{i}\omega}_{out}t} + {{\mathbb{i}\phi}_{out}{(t)}}}} - {{E_{in}(t)}{\mathbb{e}}^{{{\mathbb{i}\omega}_{in}t} + {{\mathbb{i}\phi}_{in}{(t)}}}}}}{{{M_{add}(t)}{\hat{p}}_{add}} = \frac{\begin{matrix}{{{E_{out}(t)}{\mathbb{e}}^{{{{\mathbb{i}}{({\omega_{out} - \omega_{add}})}}t} + {{\mathbb{i}}{({{\phi_{out}{(t)}} - {\phi_{add}{(t)}}})}}}} -} \\{{E_{in}(t)}{\mathbb{e}}^{{{{\mathbb{i}}{({\omega_{in} - \omega_{add}})}}t} + {{\mathbb{i}}{({{\phi_{in}{(t)}} - {\phi_{add}{(t)}}})}}}}\end{matrix}}{E_{add}L_{BA}}}} & (3)\end{matrix}$L_(BA) is a complex factor whose magnitude comes from the insertion lossfrom point B to point A, and whose phase is the phase shift associatedwith the path from B to A at ω_(add). It may appear from equation 3 thatthe modulation function M_(add) (t) has eight degrees of freedom, i.e.four complex elements, but in fact for the most complicated case, whereE_(in) and E_(out) are polarization multiplexed QAM signals, only fourdegrees of freedom are needed. Some simple cases require fewer than fourdegrees of freedom. The choice of M_(add) (t) depends on {circumflexover (p)}_(add), such that the product M_(add) (t){circumflex over(p)}_(add) follows equation 3, as the examples below show.

To implement equation 3, the DSP in FIG. 5 must know the input signalenvelope E_(in) (t) as well as the required output signal E_(out) (t).While the data content for the output E_(out) (t) may be communicated tothe processor from an external data source, the methods for obtainingE_(in) (t) will be discussed below.

In this disclosure, when it is stated that “the DSP knows” a parameteror that the parameter “is known by the DSP” then this signifies that theDSP may be programmed to calculate the parameter from the data itreceives from A/D converters and from other data passed to it. It is notnecessary for the DSP to actually calculate the parameter or have itstored in one of its registers for the DSP to know the parameter. Forexample, it might be stated below that parameter B can be calculatedgiven that parameter A is known by the DSP. The designer of the DSPbeing skilled in the art will then understand how to program the DSP tocalculate parameter B. However, the designer may choose an algorithmwhich starts from the values passed to the DSP from the A/D convertersbut does not calculate parameter A as an interim value, if such analgorithm uses fewer steps than one which does explicitly calculateparameter A.

FIG. 6 illustrates an apparatus for modulating the add laser which worksin the general case, when E_(in) (t) and E_(out) (t) comprisepolarization multiplexed quadrature signals. The add laser 601 ispolarized at 45°, so

${\hat{p}}_{add} = {\frac{1}{\sqrt{2}}\begin{pmatrix}1 \\1\end{pmatrix}}$The polarization beamsplitter 602 divides the laser power equally, sothe top output 603 is horizontally polarized and the bottom output 604is vertically polarized. The Jones matrix associated with the path fromthe polarization beamsplitter input to the top output is

$\quad\begin{pmatrix}1 & 0 \\0 & 0\end{pmatrix}$and from the input to the bottom output is

$\quad\begin{pmatrix}0 & 0 \\0 & 1\end{pmatrix}$Each of the two polarization beamsplitter outputs are modulated by aquadrature modulator 605. Each quadrature modulator comprises aMach-Zehnder configuration with an amplitude modulator 606 in each arm,and where one arm has a longer path length than the other by a wholenumber of wavelengths+½ (i.e., one arm has π/2 phase shift 607 comparedto the other). The outputs of the two quadrature modulators are combinedat 608 to give the output of modulation subsystem 609. The amplitudemodulators in two arms of the top polarization beamsplitter output aredriven by voltages from the D/A converters so as to produce modulationfunctions M_(re,x) (t) and M_(im,x) (t) respectively. They arezero-chirp modulators, so M_(re,x) (t) and M_(im,x) (t) are realquantities. The transfer function of the quadrature modulatorconfiguration in the top polarization beamsplitter output path istherefore M_(re,x) (t)+iM_(im,x) (t). Similarly the two modulators inthe lower polarization beamsplitter output are driven to have transferfunctions M_(re,y) (t) and M_(im,y) (t), and the net transfer functionof the quadrature modulator is M_(re,y) (t)+iM_(im,y) (t). Eachamplitude modulator may be implemented as a zero-chirp Mach-Zehndermodulator. The transfer function of such a Mach-Zehnder modulator is ofthe form sin(πV/2V_(π)), where V is the input voltage to the modulator,and the values of the D/A converters are preferably chosen to take intoaccount this nonlinear transfer function. The outputs of the twoquadrature modulators are combined at a passive combiner stage. Theoverall transfer function of the modulator block is (aside frommultiplicative constants for the loss of the split and combine elements,which can be absorbed into L_(BA))

${{M_{add}(t)}{\hat{p}}_{add}} = {\begin{bmatrix}{{\begin{pmatrix}1 & 0 \\0 & 0\end{pmatrix}\left( {{M_{{re},x}(t)} + {i\;{M_{{im},x}(t)}}} \right)} +} \\{\begin{pmatrix}0 & 0 \\0 & 1\end{pmatrix}\left( {{M_{{re},y}(t)} + {i\;{M_{{im},y}(t)}}} \right)}\end{bmatrix}\frac{1}{\sqrt{2}}\begin{pmatrix}1 \\1\end{pmatrix}}$ ${{M_{add}(t)}{\hat{p}}_{add}} = \begin{pmatrix}{{M_{{re},x}(t)} + {i\;{M_{{im},x}(t)}}} \\{{M_{{re},y}(t)} + {i\;{M_{{im},y}(t)}}}\end{pmatrix}$Hence values may be passed to the D/A converters to set M_(re,x) (t),M_(im,x) (t), M_(re,y) (t) and M_(im,y) (t) to give the requiredmodulation function of equation 3.

The configuration of FIG. 6 may consist of separate fiber pigtailedcomponents, provided attention is paid to the optical phase shiftsbetween components. In the preferred embodiment of the presentinvention, an integrated version is built, such as in a planar waveguidetechnology. For example, the quadrature modulator and laser have beenintegrated in a gallium arsenide platform, as described in “10 Gb/soptical differential quadrature phase shift key (DQPSK) transmissionusing GaAs/AlGaAs integration” by R. A. Griffin et al. (OFC 2002conference, Anaheim, US, paper FD6, 2002).

Many variations of the configuration shown in FIG. 6 are possible whichallow the same result, to change an arbitrary signal E_(in) (t) into anarbitrary E_(out) (t). For add laser SOPs other than linear 45° it istrivial to find splitting arrangements that allow separate modulation oftwo orthogonal polarization components.

The amplitude modulators of FIG. 6 may be modulators which have chirp.Given that the chirp characteristic is known, it is possible to set theD/A voltage outputs to obtain an arbitrary modulation. The correctmodulation function may be obtained if the two arms of the quadraturemodulator do not have exactly π/2 phase difference, given that the phasedifference is known by the DSP, and it is not close to 0 or π. Thequadrature modulation function may be achieved using a combination ofmodulators other than a pair of modulators in arms of a Mach Zehnderconfiguration. For example, an amplitude modulator followed by a phasemodulator provides the quadrature modulation function, but unless anendless phase modulator is used this combination does not offer endlessphase adjustment, as is discussed below. Similarly, there areconfigurations of modulators other than the polarization diverseconfiguration of FIG. 6 which may achieve the required modulationfunction. For example, a sequence of two polarization modulators whichoperate on different polarization axes, an amplitude modulator and aphase modulator, may perform the task.

The configuration of FIG. 6 may also perform endless modulation of thephase and state of polarization. In alternate embodiments of the presentinvention, configurations may not offer endless phase and/orpolarization modulation. This means that the output electric fieldenvelope E_(out) (t) takes on the desired value at all times t at thecentre of a symbol, but there could be an occasional additional cycle ofphase or polarization between adjacent symbol centers. It depends on theoverall system design whether such extra cycles cause a degradation inperformance. The extra cycles broaden the spectrum of the signal, whichmay cause crosstalk in a dense WDM channel plan. This may cause animpairment when combined with fiber propagation effects.

U.S. Patent Application No. 2004/0067064, U.S. Patent Application No.2004/0105682 and U.S. Patent Application No. 2005/0007642 discloseoptical transmitters where a laser is modulated by a modulationsubsystem whose analog drive voltages are set by a digital signalprocessor via D/A converters. The modulation subsystems in thesedisclosures are capable of setting the inphase and quadrature parts ofboth states of polarization of the electric field envelope. These priorart disclosures are different from the present invention in that in theprior art disclosures the electric field envelope is chosen toprecompensate for a fiber propagation impairment, whereas in the presentinvention the electric field envelope of the add signal is chosen toproduce the desired output signal electric field envelope when the addsignal is combined with the input signal.

A. Monitoring of Input and Output Signals

As discussed above, the description of coherent channel substitutiondoes not cover how the input signal electric field is known to the DSP.FIG. 7 illustrates an arrangement which adds monitors for the input andoutput signals to the apparatus of FIG. 5. The monitors tap light fromthe main optical fiber by splitters 701 and 707. The input monitor 702and output monitor 708 are sampled coherent detection receivers. Thelocal oscillator 703 for the input monitor is split from the add laserat splitter 705. The output monitor LO may or may not be split from theadd laser. However, it is cost-effective to do this if the outputmonitor is at the same location as the add laser. (The connections fromthe DSP 507 to the input and output monitors and the modulationsubsystem 506 are shown as gray strips with arrows 709. For simplicityof the diagrams, this notation is used in FIG. 7 and in later figures.The grey strip means that several analog voltages are read by the DSPvia A/D converters or are set by the DSP via D/A converters. Thedirection of the gray arrow indicates whether voltages are set or read.)The input monitor allows E_(in) (t) e^(i(ω) ^(in) ^(−ω) ^(add) ^()t+i(φ)^(in) ^((t)−φ) ^(add) ^((t))) to be know by the DSP, through applicationof equation 2. If the add laser is used as the LO, then the outputmonitor allows the DSP to know the actual value of E_(out) (t) e^(i(ω)^(out) ^(−ω) ^(add) ^()t+i(ω) ^(out) ^((t)−φ) ^(add) ^((t))) and, afterapplying a phase estimate, the actual value of E_(out) (t) (which maynot be exactly the same as the desired values). Note that E_(in) (t)e^(i(ω) ^(in) ^(−ω) ^(add) ^()t+i(φ) ^(in) ^((t)−φ) ^(add) ^((t))) andthe desired value of E_(out) (t) e^(i(ω) ^(out) ^(−ω) ^(add) ^()t+i(φ)^(out) ^((t)−φ) ^(add) ^((t))) are the quantities needed to calculatethe add modulation function via equation 3.

If the coherent signal substitution arrangement is being used as part ofan add-drop node, then the input monitor can also be the detector thatreceives the drop channel.

A data connection 710 is shown in FIG. 7 providing an input to thedigital signal processor. This connection supplies the data values thatconstitute the information in E_(out) (t). When the coherent channelsubstitution system is acting as a regenerator then the output data istaken from the input data, as discussed below.

There is a delay element 704 between the tap to the input monitor (pointC) and the add coupler (A), and a delay element 706 between the addlaser (B) and the add modulator subsystem (E). These optical delays maybe implemented via optical fiber delay lines or delay lines in a planarwaveguide platform. The first delay is present because the transit timefrom C to A has to match the processing delay, and realistically ittakes time for the DSP to compute E_(in) (t) e^(iω) ^(in) ^(t+iω) ^(in)^((t)), and time to calculate the required values of the D/A convertersto obtain the required add signal modulation function. Let τ_(com) bethe total time for an optical signal to cross point D, be detected,undergo computation, and modulation to be applied to an optical signalwhich travels to point E. Let the transit time for an optical signalfrom C to A be τ_(CA), and similarly for τ_(CD) and τ_(EA). The opticaldelay τ_(CA) should be such thatτ_(CA)≈τ_(CD)+τ_(com)+τ_(EA)  (4)where the approximate equality sign means that the left hand and righthand sides of equation 4 correspond to within a small fraction of asymbol period. It may ease the design to make the optical delay longerthan the expected processing delay, and to include an elastic bufferwithin the DSP which may be adjusted to make the delays match, andperhaps to have a clock phase adjustment on the clock controlling theD/A converters.

There is a delay between the add laser and the modulator in order toensure that the phase of the add laser at a certain symbol in the inputsignal, as included in the measurement made by the input monitor, hasnot drifted when modulation is applied by the add laser modulationsubsystem at that symbol. The requirement on the delays isτ_(BE)≈τ_(com)+τ_(BD)  (5)where the approximate equality sign means that the left hand and righthand sides of equation 5 correspond to within a fraction of thecoherence time of the add laser. The coherence time is 1/(add laserlinewidth). This delay 706 can therefore be set with less accuracy thanthe first delay 704. If the add laser linewidth is sufficiently narrow,then equation 5 may be satisfied by the natural delay from B to E,without the need for a specific delay element.

If the optical delay between the input monitor and the add coupler isexactly known, if the optical connections in FIG. 7 are polarizationmaintaining, and if the characteristics of the add laser modulationstage are known, then equation 3 may be satisfied without an outputmonitor. In practice the phase lengths of the delays within theapparatus will not be initially known, and they will vary slowly withtemperature. Additionally, the SOP of the add signal may drift comparedto the optical signal to be substituted. An output monitor may deducethe errors in these phase lengths and SOPs and feed the result back tothe part of the digital signal processor that computes the D/A values.In this document the optical phase and state of polarization of anoptical signal may be referred to as basic parameters of the opticalsignal. The output monitor may also determine if any other parameters ofthe add laser modulation subsystem are in error and correct them, suchas the phase difference between arms of the quadrature modulators, thefrequency response of the modulation electro-optics, etc. The outputmonitor does not have to be located close to the add laser modulationsubsystem. The output monitor could be located at a remote sitedownstream. For example, the sampled coherent detection operation at thereceive end of the link may be used as the output monitor of FIG. 7also. This may save equipment cost, but may mean that messages wouldhave to be sent continuously between the receive site and the add site,and parameter changes within the add modulator subsystem that change tooquickly could not be tracked.

FIG. 7 illustrates a preferred embodiment of the invention where thelocal oscillator for the input monitor sampled coherent detection unitis taken directly from the add laser. It is possible for the inputmonitor LO not to come directly from the add laser, provided that thephase and polarization relationship between the input monitor LO and theadd laser is known by the DSP. In an alternative embodiment of thepresent invention, the LO for the input monitor is an independent laser,and there is an additional sampled coherent detection unit which beatsthe input monitor LO with the add laser to deduce the phase relationshipbetween them and pass it to the DSP. In another alternative embodimentone or more frequency-stabilized octave-spanning optical combs are used.The LO for the input monitor is an independent laser and it is beatagainst a frequency-stabilized octave-spanning comb in a sampledcoherent detection apparatus to find the phase relationship between theLO and a proximate line in the comb. The add laser is also beat againsta frequency-stabilized octave-spanning comb to find the phaserelationship between the add laser and a proximate line in the comb. Thephase relationship between the add laser and the input monitor LO maythen be deduced. The frequency-stabilized octave-spanning optical combhas been developed recently, and is described in “Optical frequencymetrology,” by T. Udem et al. (Nature, vol. 416, p. 233-237, 2002),incorporated herein by reference. It has the property that all spectrallines in the comb have an optical frequency which is an exact multipleof a known radio frequency and the spectral lines contain no phasenoise.

FIG. 7 illustrates the output monitor in a preferred embodiment of thepresent invention. The output monitor in the preferred embodiment is asampled coherent detection unit. The primary purpose of the outputmonitor is to provide an indication to the DSP when the optical phase orSOP of the add laser have departed from their intended values. It ispossible to obtain such an indication using methods other than bysampled coherent detection, as is understood by those skilled in theart. In an alternative embodiment that is suitable for use with BPSK orQPSK signals, the output monitor contains a single detector which worksin direct detection mode. The output monitor may also contain a passiveoptical bandpass filter to select only the WDM channel beingsubstituted. The detected electrical spectrum contains a component atthe symbol clock frequency, and by feeding the size of that componentback to the DSP, it can be ensured that the DSP has the correct valuesfor the add laser phase and SOP. When these values are correct thecomponent of the detected electrical spectrum at the symbol clockfrequency will be at a minimum, and a departure from the minimumindicates that the values are not correct.

By applying monitoring and add laser modulation that implements equation3 exactly, the output signal is the desired signal Re└E_(out) (t) e^(iω)^(out) ^(t+iφ) ^(out) ^((t))┘. In practice, the input monitor is notperfect and introduces noise and distortions due to the detector noise,finite A/D resolution, and other causes. Let the difference between theinput signal recorded by the DSP and the actual input signal be Jonesvector n_(in) (t). Similarly, the output electric field of the add laserdiffers from that specified by the DSP because of finite D/A converterresolution and other effects. The difference between the actual andspecified modulated add laser electric fields is denoted by n_(out) (t).Thus, the actual output of the coherent channel substitution subsystemisRe└E_(out)(t)e^(iω) ^(out) ^(t+iφ) ^(out) ^((t))+n_(in)(t)+n_(out)(t)┘The system is preferably designed so as to minimize the noisecontributions n_(in) (t) and n_(out) (t).

U.S. Patent Application No. 2005/0008369 discloses equipment for anadd-drop node where the drop signal is observed by coherent detectionand where light from the same laser that is modulated to make the addchannel is used as the local oscillator for the coherent detection ofthe drop channel. This disclosure is substantially different from thepresent invention in that in the aforementioned patent application thedrop channel is removed from the main fiber by a passive optical filter,while in the present invention the drop channel is removed by opticalinterference with the add channel.

B. Arrangements to Work with Simple Modulation Formats

The equipment depicted in FIG. 5 and FIG. 6 is capable of substituting aWDM channel where data is modulated on both inphase and quadraturecomponents in both states of polarization. When simpler modulationformats are involved or when the resolution of the D/A converter islimited, alternative architectures may be used.

An example is the case where the input and output signals are on-offmodulated single-polarization signals. Assuming no additive noise ordistortion, the electric field takes on values of eitherE_(on){circumflex over (p)} (on state) or 0 (off state), where E_(on) isa scalar constant and {circumflex over (p)} is the Jones unit vector ofthe signal's SOP. Provided that the phase and SOP of the add laser aremade to align with the input signal, the add signal electric fieldenvelope needs to take on only three possible values: −E_(on), 0 orE_(on). A Mach-Zehnder modulator driven at −V_(π), 0 and V_(π) mayprovide this modulation. The required modulation of the add laser inthis case may thus be applied by the apparatus shown in FIG. 8, whichincludes the Mach-Zehnder amplitude modulator 802, together with phaseadjustment 801 and polarization adjustment 803 stages. Two D/Aconverters 804 are shown setting two analog voltages to control thephase adjustment and polarization adjustment stages, and in fact adifferent number of analog voltages may be needed, hence the small dotsin FIG. 8. An advantage of the configuration of FIG. 8 over theconfiguration in FIG. 6 is that only the amplitude modulator needs to bedriven at the symbol rate. The phase adjustment must be made with aresponse time much less than the coherence time of the add laser, and itmust be endless. A quadrature modulator driven by periodic waveforms π/2out of phase and an acousto-optic modulator are examples of componentsthat may provide an endless phase shift. The polarization must beadjusted faster than the rate of change of the incoming signal SOP. Anendless polarization adjuster may be made from a series of waveplates,as described in “Polarization control for coherent communications,” byN. G. Walker & G. R. Walker (IEEE J. Lightwave Technol., vol. 8, no. 3,p. 438-458, 1990).

When the modulation format of the input and output optical signals issingle polarization BPSK, then the add signal electric field envelopeneeds to take on only two values, −E_(on) or E_(on). The arrangement ofFIG. 8 is suitable for this case also, where the amplitude modulator isdriven at one of two voltages: −V_(π) and V_(π).

In a typical add-drop situation the incoming signal contains additivenoise. The best solution with respect to optical transmission quality isto have a high resolution D/A converter driving the Mach-Zehndermodulator, and to set the D/A converter so as to cancel the incoming(drop) signal+noise, as well as insert the outgoing signal. The outputsignal then contains minimal noise in its inphase component. However, itmay be preferable to use a low resolution D/A converter, perhaps becausesuch a component costs less or is available with higher bandwidth. Thelowest resolution D/A converter that can be used has the same number ofstates as the add signal, that is three states in the example of on-offmodulated input and output signals, or two states in the example of BPSKmodulated input and output signals. The add-drop function issuccessfully performed when the lowest allowable resolution D/Aconverter is used, but the additive noise on the input signal istransferred to the output signal. The transmission system design mustthen take into account that noise accumulates over the whole length ofthe link.

The apparatus of FIG. 7 has the endless phase adjustment separate fromthe add laser, and the add laser is free running. It is possible toeffectively achieve endless phase adjustment by modulating the drivecurrent to a semiconductor laser, or otherwise changing the laseroptical frequency. FIG. 9 shows an arrangement using direct laser phasecontrol which offers the same result as that of FIG. 7. This coherentchannel substitution system is a different architecture to the onediscussed above and depicted in FIG. 7. The add laser 505 in FIG. 9 isphase locked to the incoming signal 501 by direct modulation, that is inan optical phase locked loop (OPLL) configuration. The incoming signaland add laser (local oscillator) are mixed at 901 and unit 902 estimatesthe phase difference between them. Sampled coherent detection may beused to perform this operation, or a conventional hardware-based methodmay be used. The phase difference constitutes an error signal, which isthen filtered by a loop filter function 903, and the result applied asmodulation to the add laser. Again, if sampled coherent detection isused, the loop filter may be implemented within the DSP and the addlaser modulation voltage set by a D/A converter, or conventional analogsignal processing hardware may be used. The delay of the feedback loopmust be much shorter than the coherence time of the add laser for theoptical phase locked loop to function correctly. This constraint canforce the use of an expensive narrow linewidth add laser. There is nosuch constraint on the time to calculate a phase estimate in the firstarchitecture shown in FIG. 7, provided the delay τ_(BE) complies withequation 5.

C. Multiple Channel Architecture

In the examples of coherent channel substitution described above, forevery one WDM channel at the input, one add laser is used to make asingle WDM channel at the output. If the monitor and modulationelectro-optics have sufficient bandwidth, then several neighboring WDMchannels at the input may be modified into several output channels bymodulating a single add laser. In fact, the concept may be broadened sothat N_(in) neighboring input WDM channels are substituted by N_(out)neighboring output WDM channels, by adding N_(add) appropriatelymodulated add lasers; and where N_(in), N_(out) and N_(add) are not thesame number. Each modulated add laser occupies a certain bandwidth ofoptical spectrum. The combination of all the modulated add lasers mustoccupy a contiguous region of spectrum that covers all the N_(in) inputchannels and all the N_(out) output channels. FIG. 10 illustrates anexample of optical spectral occupancy where N_(in)=3, N_(out)=2 andN_(add)=4. The horizontal direction in FIG. 10 represents increasingoptical frequency. The input channels are blocks 1001; the add channelsare blocks 1002, and the output channels are blocks 1003. If thebandwidth of an input channel is B_(ch,in), and similarly B_(ch,out) forthe output and B_(ch,add) for the modulated add channels; the guardbandwidth between input channels is B_(guard,in), and similarlyB_(guard,out) between output channels; and the overlap bandwidth ofneighboring add channels is B_(overlap,add), then it is required thatN _(add) B _(ch,add)−(N _(add)−1)B _(overlap,add) ≧N _(in) B _(ch,in)+(N_(in)−1)B _(guard,in)and for the output channels (assuming they are centered on the inputchannels)N _(add) B _(ch,add)−(N _(add)−1)B _(overlap,add) ≧N _(out) B_(ch,out)+(N _(out)−1)B _(guard,out)

Using a notation where the input WDM channel parameters are labeled witha subscript, so kth channel has electric field Re└E_(in,k) (t) e^(iω)^(in,k) ^(t+iφ) ^(in,k) ^((t))┘, and similarly for the output and addchannels, the combined input electric field is

${Re}\left\lbrack {\sum\limits_{k = 1}^{N_{in}}{{E_{{in},k}(t)}{\mathbb{e}}^{{{\mathbb{i}\omega}_{{in},k}t} + {{\mathbb{i}\phi}_{{in},k}{(t)}}}}} \right\rbrack$The desired output electric field is

${Re}\left\lbrack {\sum\limits_{k = 1}^{N_{out}}{{E_{{out},k}(t)}{\mathbb{e}}^{{{\mathbb{i}\omega}_{{out},k}t} + {{\mathbb{i}\phi}_{{out},k}{(t)}}}}} \right\rbrack$To obtain this desired output, the kth of the add lasers is modulated bya M_(add,k) (t){circumflex over (p)}_(add,k) product, such that

$\begin{matrix}{{\sum\limits_{k = 1}^{N_{add}}{{M_{{add},k}(t)}{\hat{p}}_{{add},k}E_{{add},k}L_{{BA},k}{\mathbb{e}}^{{{\mathbb{i}\omega}_{{add},k}t} + {{\mathbb{i}\phi}_{{add},k}{(t)}}}}} = {{\sum\limits_{k = 1}^{N_{out}}{{E_{{out},k}(t)}{\mathbb{e}}^{{{\mathbb{i}\omega}_{{out},k}t} + {{\mathbb{i}\phi}_{{out},k}{(t)}}}}} - {\sum\limits_{k = 1}^{N_{in}}{{E_{{in},k}(t)}{\mathbb{e}}^{{{\mathbb{i}\omega}_{{in},k}t} + {{\mathbb{i}\phi}_{{in},k}{(t)}}}}}}} & (6)\end{matrix}$in analogy with equation 3.

The apparatus of FIG. 11 is able to perform coherent channelsubstitution for multiple wavelength channels. The apparatus containsthe features of FIG. 7, with some of those features present multipletimes. There are three add lasers 1105 shown in FIG. 11. Additionally,in alternate embodiments, there may be any number of add lasers. Copiesof the add lasers 1103 go to the add laser phase comparison unit 1104,which uses sampled coherent detection to determine the phases of the addlasers with respect to one another. It is convenient mathematically touse one laser as the reference, such as add laser 1. The add laser phasecomparison unit provides this information to the DSP(ω_(add,k)−ω_(add,l))t+φ _(add,k)(t)−φ_(add,l)(t) for k=2 . . . N _(add)The input monitor 1101 uses one or more sampled coherent detection unitsto record the combined input electric field. The local oscillators 1102are provided by the add lasers. The number of sampled coherent detectionunits required depends on the bandwidth of the detection electro-opticsand A/D converter, that is how much optical spectral bandwidth eachsampled coherent detection unit can see. Even if several sampledcoherent detection units are employed, and hence several add laser LOs,given that the phases of the add lasers relative to one another areknown, the input electric field compared to add laser 1 may be recordedwithin the DSP as

$\sum\limits_{k = 1}^{N_{in}}{{E_{{in},k}(t)}{{\mathbb{e}}^{{{{\mathbb{i}}{({\omega_{{in},k} - \omega_{{add},1}})}}t} + {{\mathbb{i}}{({{\phi_{{in},k}{(t)}} - {\phi_{{add},1}{(t)}}})}}}.}}$The add lasers each send light into a modulation subsystem 1106 in asimilar fashion as that for the single add laser case, having modulationfunction M_(add,k)(t){circumflex over (p)}_(add,k). The modulatedoutputs are combined in the add laser combiner 1107. Point A and severalpoints B are marked in FIG. 11, associated with several values ofL_(BA,k).

The function of the output monitor is to feed back values of parametersin the modulation subsystems, as in the single wavelength case.Preferably, the output monitor 1108 comprises a number of sampledcoherent detection units whose local oscillators may be provided by theadd lasers like the input monitor. In an alternative embodiment, theoutput monitor is a single sampled coherent detection unit and has onelocal oscillator which tunes in wavelength. By moving the LO betweenwavelengths so as to cover the whole of the relevant optical bandwidth,information may be obtained about the deviation of each of the addlasers in optical phase or SOP from the value assumed by the DSP. The LOmust rove sufficiently quickly to avoid a substantial drift in opticalphase or in SOP from any one add laser.

FIG. 12 illustrates a preferred embodiment of the add laser phasecomparison unit. The configuration of FIG. 12 provides a simple way toimplement the sampled coherent detection operation to obtain the addlaser phases relative to one another. Light from the add lasers 1103 iscombined in the passive combiner 1201 and then detected in the singlephotodetector 1202 and optionally amplified at 1203. The spectralspacing between the add lasers is staggered, so that there are N_(add)−1distinct tones in the photocurrent of the photodetector at frequenciesclose to the average difference frequency (plus other higher frequencybeat products that are filtered out). The beat products may then bedownshifted using a radio frequency (r.f.) mixer 1204, so that thesingle A/D converter 1206 has a lower bandwidth and is run at a lowersampling rate than if the r.f. mixer were absent. The DSP 1207 is ableto extract the phase and frequency information of the add lasersrelative to one another based on the phase and frequency of thedifferent beat tones, together with the frequency of the oscillator 1205that drives the r.f. mixer.

FIG. 11 can be considered as a high level diagram showing the elementsneeded to implement coherent channel substitution with multiplewavelength channels. In fact there are many ways to arrange thedifferent elements so that the DSP may calculate modulation functionsfor the add lasers and the appropriate modulation may be applied.Solutions are possible where the functions represented by the blocks inFIG. 11 are separated and grouped in other ways. For example, FIG. 13shows an architecture which appears different from that of FIG. 11,where the input monitor function and the add laser combiner function areimplemented in a distributed manner. There are two add laser combiners1302 and 1304, and two input monitors 1301 and 1303 in the example ofFIG. 13. All the solutions have the following in common: the digitalsignal processor has knowledge of the phases of the add lasers withrespect to one another, the electric fields of the input WDM channelswith respect to the add lasers and the desired output electric fieldwith respect to the add lasers; and the digital signal processor acts onmodulation components via D/A converters so that the electric field ofthe modulated add lasers which superimposes on the input electric fieldis able to effect the required channel substitution. The second inputmonitor 1303 in line sees a signal which is different from the inputsignal 501 in that a portion of the optical spectrum has been replacedby coherent interference at the first combiner 1302. The signal seen bythis input monitor partially corresponds to the input signal 501. TheDSP may know the input signal electric field envelope by assembling datafrom all the input monitors, even if the individual input monitors seesignals which only partially correspond to the input signal. Similarly,the output monitor may be distributed, and the individual outputmonitors may see signals which partially correspond to the output signal504. It is possible for a sampled coherent detection unit to perform therole of both an input monitor and an output monitor.

To calculate the N_(add) different M_(add,k) (t){circumflex over(p)}_(add,k) functions, the spectrum of the composite input and desiredoutput electric field is divided into sections. A one-sided stitchingfunction G_(os) (ω) is chosen which has the property thatG _(os)(ω)=10≦ω≦π(B _(ch,add)−2B _(overlap,add))G _(os)(ω)=1−G _(os)(2π(B _(ch,add) −B _(overlap,add))−ω)π(B _(ch,add) −B _(overlap,add))<ω≦πB _(ch,add)G _(os)(ω)=0ω>πB _(ch,add)  (7)The raised cosine family of functions are examples of functions whichcomply with equation 7. Out of G_(os) (ω) three two-sided stitchingfunctions are formed. The low frequency add laser uses G_(l) (ω), whereG _(l)(ω)=1ω<0G _(l)(ω)=G _(os)(ω)ω≧0The high frequency add laser uses G_(h) (ω)G _(h)(ω)=G _(os)(−ω)ω≦0G _(h)(ω)=1ω>0The intermediate add lasers use G_(m) (ω)G _(m)(ω)=G _(os)(−ω)ω<0G _(m)(ω)=G _(os)(ω)ω>0Examples of the three two-sided stitching functions are given in FIG.14. FIG. 14 a shows a possible shape of the transfer function 1401versus optical frequency G_(l) (ω); FIG. 14 b shows the transferfunction 1402 G_(m) (ω); and FIG. 14 c shows the transfer function 1403G_(h) (ω). They have the required property that the sum of the N_(add)stitching functions, frequency shifted by the respective add lasercentre frequency, is flat and equal to 1.

The spectrum required of an add laser, the Kth add laser for example,after modulation is given by multiplying the Fourier transform of therequired electric field difference on the right hand side of equation 6by the appropriate stitching function G_(K) (ω) (which is one of G_(l)(ω), G_(m) (ω) or G_(h) (ω) depending on whether K is a low, middle orhigh frequency channel). This operation is equivalent to the operationin the time domain of convolving the required electric field differencewith the stitching function's impulse response g_(K) (t), the inverseFourier transform of G_(K) (ω). The required modulated output of the Kthadd laser is therefore

$\left( {{\sum\limits_{k = 1}^{N_{out}}{{E_{{out},k}(t)}{\mathbb{e}}^{{{\mathbb{i}\omega}_{{out},k}t} + {{\mathbb{i}\phi}_{{out},k}{(t)}}}}} - {\sum\limits_{k = 1}^{N_{in}}{{E_{{in},k}(t)}{\mathbb{e}}^{{{\mathbb{i}\omega}_{{in},k}t} + {{\mathbb{i}\phi}_{{in},k}{(t)}}}}}} \right) \otimes {g_{K}(t)}$which is obtained by a modulation function

${{M_{{add},K}(t)}{\hat{p}}_{{add},K}} = \frac{\begin{pmatrix}{{\sum\limits_{k = 1}^{N_{out}}{{E_{{out},k}(t)}{\mathbb{e}}^{{{{\mathbb{i}}{({\omega_{{out},k} - \omega_{add}})}}t} + {{\mathbb{i}}{({{\phi_{{out},k}{(t)}} - {\phi_{add}{(t)}}})}}}}} -} \\{\sum\limits_{k = 1}^{N_{in}}{{E_{{in},k}(t)}{\mathbb{e}}^{{{{\mathbb{i}}{({\omega_{{in},k} - \omega_{add}})}}t} + {{\mathbb{i}}{({{\phi_{{in},k}{(t)}} - {\phi_{add}{(t)}}})}}}}}\end{pmatrix} \otimes {g(t)}}{E_{add}L_{BA}}$The convolution operation may be performed in the DSP as a finiteimpulse response filter. Only a subset of the N_(in) input channels andN_(out) desired output channels will contribute to the result for agiven add laser, and so the others may be omitted from the sums. Thevoltages to deliver to the modulation subsystem are obtained fromM_(add,K)(t){circumflex over (p)}_(add,K) in the same way as for a thesingle channel case.D. Configurations using Coherent Channel Substitution

There are several configurations in a fiber optic transmission networkwhere coherent channel substitution may be employed. Some of theseconfigurations are listed below.

1. WDM Add-Drop

In this case one WDM channel is dropped at a node and another channel ofthe same wavelength is added. Multiple channels may be added or dropped.The main add-drop functions, that is the input monitor and add channelmodulation of FIG. 7, may be located at the add drop node as in FIG. 1e, or at the end of a spur such as is depicted in FIG. 1 d. The lengthof the spur cannot be so long that the delay τ_(CA), as specified byequation 4, becomes unmanageable.

The output signal may be a different modulation format or symbol ratefrom the incoming signal. The bandwidth of the D/A converters andelectro-optics in the add laser modulation subsystem must be wide enoughto cope with the higher of the symbol rates of the input signal andoutput signal. If the channel to be added has a higher symbol rate thanthe channel dropped, then there must be sufficient spectral bandwidthbetween any neighboring channels to accommodate the new higher bandwidthchannel.

2. WDM Drop Only

In some applications of a drop node, as drawn in FIG. 1 c, it may berequired that the signal continuing towards the receive end of the linkbe extinguished. This would be a requirement if there is an add nodedownstream at the same wavelength which is of a simple design using onlya tap coupler to add the new signal, i.e. without hardware for anothercoherent channel substitution operation. Alternatively, it may berequired to remove the superfluous signal to reduce the optical powerlevel so as to save on the cost of downstream optical amplification orto reduce the crosstalk experienced by the remaining useful WDMchannels.

The extinction of the drop channel may be achieved with the coherentchannel substitution arrangement by settingE _(out)(t)=0

3. Digital Regenerator

The purpose of digital regenerator is to receive a digital signal afterit has experienced additive noise and/or distortion, to make a decisionwhich digital symbol value was sent for each symbol slot, and thentransmit a sequence of clean symbol values free of noise and distortion.If the digital signal is encoded by a forward error correction (FEC)code, then the regenerator can decode the FEC to get a better estimateof the true symbol values, and subsequently transmit those values in FECencoded form. In addition, a digital regenerator may modify overheadbits, for example to record the number of bit errors it has counted.

The digital regenerator function for a WDM channel may be implemented asa variation of the WDM add-drop case, where the information to be addedis the same as the information dropped.

The coherent channel substitution process may implement a usefulcompensation feature for fiber propagation effects beyond what may bedone by a conventional digital regenerator. With some fiber optictransmission systems the fiber propagation effects are managed, forexample using chromatic dispersion compensation, such that the signalappearing at the receive end is sufficiently undistorted to detect itwith low bit error rate (BER). However, the signal may be stronglydistorted if observed at intermediate locations. This signifies that thefiber propagation management scheme may have to be modified to insert aregenerator at an intermediate point. With the coherent channelsubstitution regenerator the appropriate compensation for theaccumulated propagation effects from the transmitter to the regeneratorsite may be applied after detection within the DSP. Then anothertransform may be applied before calculating the D/A converter values, sothat the signal that leaves the regenerator is predistorted to take intoaccount the path from the regenerator site to the receiver, but is inother respects a regenerated signal. The signal that arrives at thereceive end of the link thus shows minimal distortion.

4. Tributary Add-Drop

A high bit rate signal is typically composed of many tributaries. Thesemay be organized within the signal as packets, that is contiguous blocksof bits; by time interleaving of bits or bytes; or as part of a complexmultiplexing structure, such as plesiochronous digital hierarchy. It maybe required to perform an add-drop operation on some tributaries of aWDM signal, and leave other tributaries to continue. This operation maybe performed by extracting the drop tributary information from the dropchannel detector, and calculating E_(out) (t) so that it contains therequired through tributaries and add tributaries.

5. Optical Phase Lock

There are applications where one laser, the slave, is to be made to havean optical frequency and optical phase that follows another laser, themaster. Usually this is done via an optical phase locked loop. An OPLLwas described above, as a component of an alternative configuration toachieve coherent channel substitution. It was noted that an OPLL isdifficult to implement. It comprises a feedback loop which must have ashort delay time and wide bandwidth. This forces the use of expensivecomponents, and may prohibit using DSP technologies.

The coherent channel substitution method, excluding the option describedabove using an OPLL, provides an alternative way to achieve opticalphase lock. The apparatus to achieve phase lock is illustrated in FIG.15. There is no feedback loop, so this method cannot be classed as aphase locked loop. However, it does achieve the phase lock condition.The fact that there is no feedback eases the design, since it is thetight tolerances of the feedback loop that makes an OPLL difficult toimplement. Some light from laser 1504 is used as a local oscillator 1503for the sampled coherent detection unit 1502 which observes the inputsignal (the master) 1501. The DSP 1506 receives information from thesampled coherent detection unit, and then controls the endless phaseadjustment 1507, which modifies the phase of light from the laser. Theoutput 1508 of the endless phase adjustment is the phase locked output,a slave of the input. In this embodiment of the present invention thereis no need to combine this signal with the input signal as there was forthe previous embodiments. The arrangement of FIG. 15 is the same as thatof FIG. 7 where the connection in the main fiber from the input monitorsplitter 701 to the combiner 502 has been removed. Laser 1504 has thesame role as the add laser 505, and the endless phase adjustment 1507has the same role as the modulation subsystem 506 of FIG. 7. The laseris made to have a c.w. output that is phase locked to the input bysettingM _(add)(t){circumflex over (p)} _(add)=(constant)e ^(i(ω) ^(in) ^(−ω)^(add) ^()t+i(φ) ^(in) ^((t)−φ) ^(add) ^((t)))where M_(add) (t){circumflex over (p)}_(add) is here the transferfunction of the endless phase adjustment. The constraint on time delaysof equation 5 still applies, to within a small fraction of the lasercoherence time.τ_(BE)≈τ_(com)+τ_(BD)  (5)This is the reason for the delay 1505. The input signal can be modulatedor c.w. The DSP makes use only of the recovered phase information(ω_(in)−ω_(add))t+φ_(in)(t)−φ_(add)(t), and does not use the amplitudeinformation in the case where the input signal is modulated.

U.S. Pat. No. 6,810,048 discloses an apparatus to achieve optical phaselock where a sideband to the slave laser optical frequency is generatedby a single sideband modulator, and the frequency offset and phase ofthe sideband is controlled to be phase locked to the input signalmaster. This patent does not explain how the sideband frequency andphase are controlled to be phase locked to the master, but disclosesthat the sideband offset frequency is generated by a microwaveoscillator. It is apparent from this patent that the sideband offsetfrequency must be a certain minimum value, since an electrical 90°hybrid driven at the offset frequency is used within the single sidebandmodulator, and such a component is not available that operates down to 0Hz offset. In the aspect of the present invention where it is used togenerate a phase locked optical slave signal, the endless phaseadjustment 1507 is not driven by an oscillator. Instead it is driven byone or more analog voltages that are calculated by the DSP based on thephase difference between the laser 1504 and the input signal. Tounderstand that these analog voltages cannot be considered to have comefrom an oscillator, the case where the phase difference between thelaser and the input signal does not change over a period of time isconsidered. In that case the analog voltages driving the endless phaseadjustment is constant over that period of time in consequence. U.S.Patent Application No. 2004/0208643 also discloses a way to phase lockthe sideband of an optical carrier to a master input signal. In thatdisclosure a feedback loop configuration is used, which is similar tothe standard method of achieving optical phase lock and is distinct fromthe present invention, which does not use feedback.

6. High Bandwidth Waveform Generation

To generate an optical signal modulated with a rapidly varying envelopenormally requires a high bandwidth optical modulator. Coherent channelsubstitution offers an alternative way, by modulating several carrierswith different parts of the required total optical spectrum, and thencombining them. Each carrier requires a correspondingly lower bandwidthmodulation subsystem. If the desired output signal envelope is E_(out)(t), then the multiple channel architecture of coherent channelsubstitution is implemented per equation 6 withE _(in,k)(t)=0for all k. The components to combine the input signal with the modulatedadd signals are not needed, as shown in FIG. 16. Add lasers 1601 areeach modulated by a modulation subsystem 1603, whose outputs arecombined in combiner 1604 to form the output high bandwidth waveform1606. Some light from the add lasers is delivered to a phase comparisonunit 1602, which uses sampled coherent detection so that the DSP 1607can determine the phases of the add lasers with respect to one another.The DSP sets the analog voltages of the modulation subsystem inaccordance with equation 6 as described above. The output monitor 1605has the same function as discussed in relation to the output monitor ofFIG. 11.

The configuration of FIG. 16 is similar to FIG. 11 where the inputsignal, the input signal monitor, and the main fiber up to the point ofcombination with the add laser light are not present. Additionally, theconfiguration of FIG. 16 is similar to the basic configuration of FIG.5, with the first branch of the combiner 1604 being considered ascontaining the input signal 501, and the remaining branches of thecombiner 1604 after being combined corresponding to combiner 502.

This approach allows an arbitrary signal envelope to be generated. Thecarrier still contains phase noise, which may be set to be equal to thephase noise of any one of the add lasers. Alternatively, if the phasesand frequencies of the add lasers are known compared to one of the linesin a frequency-stabilized octave-spanning optical comb, then thewaveform that is synthesized may be made to have an exact centrefrequency compared to the reference radio frequency without phase noise.The optical carrier is then locked to the envelope. The phases of theadd lasers may be found by beating at least one of them with theoctave-spanning comb in a sampled coherent detection operation, or byusing lines filtered from the comb in place of the add lasers.

E. Optical Domain Encryption

The secret optical communications aspect of the present invention isimplemented by using the apparatus of FIG. 7 where the input signal islight from a broadband optical noise source, and the substituted WDMchannel contains the information to be securely transmitted. At allpoints downstream the spectrum of the light appears broad and flat, asif it consisted entirely of optical noise. The coherent channelsubstitution method may effectively carve a notch in the noise spectrumthat is the correct shape for the information-bearing signal, and theninsert the signal in its place. FIG. 17 illustrates the spectrum 1701 ofthe optical noise effectively after a notch has been carved, and thespectrum 1702 of the channel to be added. Since broadband optical noisesources are available with 4000 GHz bandwidth, and a conventional 10Gb/s optical signal occupies about 10 GHz bandwidth, the optical signalbecomes hard to identify out of the numerous “noise” channels.Furthermore, the information-bearing channel may undergo frequencyhopping, so that the eavesdropper must continually reidentify it toextract any information. The information-bearing channel may bedisguised to appear similar to a spectral slice of optical noise. Thiscombination of features make it unfeasible for an eavesdropper to obtainthe transmitted information. The frequency hop plan and the exactalgorithm used to disguise the information to appear like noise arederived from the secret key. The intended recipient, who knows the key,can then read the information.

In a preferred embodiment of the present invention, the broadbandoptical noise source is implemented by an optical gain medium withoutfeedback (i.e., an optical amplifier with a terminated input).Alternative optical noise sources may be used, for example based onsupercontinuum generation. Any source of apparently random electricfield over a broad optical spectrum may be used as the optical noisesource. The DSP executes the coherent channel substitution via equation3 where the electric field envelope E_(out) (t) is set to equal thedesired envelope to carry the data (modified by the noise-renderingfunction described below). ω_(in) and ω_(add) are time varyingquantities according to the frequency hop sequence.

At the end of a frequency hopping interval, the add laser must be tunedrapidly to the next optical frequency in the predetermined frequency hopsequence. If the add laser is not capable of such rapid tuning then two(or more) lasers may be configured in parallel, and one of these lasersmay be selected by a fast optical switch. The unused laser is tunedduring the interval between frequency hop events, while the laser in usemaintains its optical frequency.

The optical transmission system must support transmission of thebroadband noise spectrum as though it contains information-bearingchannels. If the optical signal-to-noise ratio of the link is not highenough, the optical noise can be filtered to a narrower opticalspectrum, and the resulting reduction in the broadband noise opticalbandwidth reduces the level of security to some extent. The detectionmethod must be able to effectively select a WDM channel from itsneighbors with no guard band, which is possible, for example, by usingcrosstalk subtraction in the DSP, as described in U.S. PatentApplication No. 2004/0114939, or by orthogonal frequency divisionmultiplexing.

1. Security Level of Optical Domain Encryption

The degree of security of the transmitted message using the method ofthe present invention may be estimated and compared to other opticaldomain encryption methods. First, the security level of frequencyhopping alone is considered, in a configuration where one channel istransmitted. There is an improvement in security because theeavesdropper is forced to deploy N_(ch) times as much receivingequipment as the intended recipient, where N_(ch) is the number ofpossible frequency hop channels. It is easiest to design the systemwhere the average time spent at each frequency is more than a digitalsymbol length (slow frequency hopping), but it may be less than a symbollength (fast frequency hopping).

Second, the case is considered where a number N_(dum) dummy channelscarrying fake information are transmitted in addition to the oneinformation-bearing channel (or equivalently other differentinformation-bearing channels are added if there is need for them). Thissecond scheme is more secure than the first scheme with only onechannel. If the time spent at each frequency is τ_(h) (which does nothave to be constant), the symbol length is τ_(s) and the number ofbits/symbol is M_(s). The data on the information-bearing channel shouldhave the property that M_(av) consecutive bits must be receivedcorrectly to be able to reconstruct any of the message. This propertymay be imposed by applying a code to the data which has a long avalanchelength. In order for a receiver to be able to recover any informationM_(av)/M_(s) consecutive symbols or M_(cor) consecutive FH intervalsmust be received correctly, where

$M_{cor} = \frac{M_{av}\tau_{s}}{M_{s}\tau_{h}}$Thus, the eavesdropper must try many permutations of concatenated FHsegments to find the correct one, where the number of permutations isnumber of permutations=(N _(dum)+1)^(M) ^(cor)   (8)For each permutation the eavesdropper must examine the apparentlyreceived message to decide whether it is a genuine message, whichrequires some processing. By arranging for N_(dum) and M_(cor) to belarge, this number may be made so large that breaking the code this wayis impracticable. However increasing N_(dum) does involve the expense ofdeploying dummy transmitters that do not carry useful information. Thesecret communications scheme of the present invention is equivalent tousing the broadband optical source to emulate a large number of dummychannels packed without guard bands between them. In fact the number ofdummy channels becomes the maximum possibleN _(dum) =N _(ch)−1The number of permutations of equation 8 becomesnumber of permutations=N_(ch) ^(M) ^(cor)which may be an extraordinarily large number using modest designparameters for N_(ch) and M_(cor). The broadband optical noise source iscost effective compared to even a moderate number of dummy channels,since it requires no high speed modulation components.

There is another aspect of the optical domain encryption scheme thatmakes it secure. The amount of information that the eavesdropper has tostore to attempt to crack the code is very large. The C-band of anerbium noise source has several terahertz of bandwidth which must besampled at the Nyquist rate equal to twice that bandwidth. Theresolution of the A/D converters has to be high even if the modulationformat is a binary format. The rate at which the eavesdropper processesinformation is the product of the sampling rate and the A/D converterresolution. While there are integrated circuits (ICs) available whichprocess data at high line rates, for example for forward errorcorrection processing, these ICs make a modest number of calculations onthe input and then pass it on to the devices that follow. The processingthat the eavesdropper must apply to the received data is to firstattempt symbol phase, polarization and optical phase recovery; then trya very large number of permutations of different frequency hopintervals; and then crack the codes on the underlying data. This task istoo much to be done within one IC and would occupy years (or moreprobably billions of years) duration using currently available ICtechnologies. In consequence, the raw data must be written to a slowerstorage medium and reside there until processing is complete. Thus, theeavesdropper must possess a very large amount of storage (in addition tothe computing resources) to be able to record the encrypted signal, andthis amount of storage can be made to be unfeasibly high. This featuregives the optical domain encryption method an additional degree ofsecurity over existing encryption methods, in that an eavesdroppercannot realistically even make a recording of the message to decryptlater.

An approach which can be taken by an eavesdropper to attack theencryption method is to apply processing on all of the channel slots toquickly decide which channel slots are not carrying aninformation-bearing signal, and discard any such channels. Tosuccessfully eavesdrop, a test is needed which estimates the probabilitythat a channel is carrying a true signal during a given interval. If thetest is 100% accurate then the encryption method is defeated. If it ispartially accurate then the eavesdropper can narrow the search to asubset of the channels, which could make the memory storage andprocessing time requirements feasible for the eavesdropper. Theencryption system design must therefore ensure that no test can existwhich is approximately accurate.

Any test may be based on a difference between a statistical property ofthe signal's electric field compared to true optical noise. Keeping thefrequency hop interval τ_(h) short helps ensure there cannot be a goodtest for the eavesdropper. Any function of the optical noise measuredover a finite time interval shows a range of values, that is itssampling distribution. As the observation interval τ_(h) becomesshorter, then the sampling distribution of the function becomes wider,and overlaps the sampling distribution of the same function applied to atrue signal. For example, FIG. 18 illustrates a situation where thespectral shape of the added signal does not match the shape carved outof the optical noise spectrum. FIG. 18 a illustrates the receivedoptical spectrum 1801 that might be observed, which is a smooth spectrumcontaining a ripple feature 1802 at the signal channel location. Theripple is caused by a spectral stitching error, which may be used as thebasis of a test for the eavesdropper. However, a smooth spectrum shownin FIG. 18 a is obtained after a long observation interval (assuming thesignal stays at the same channel). After a short observation interval aspectrum such as the received spectrum 1803 of FIG. 18 b is observed.The stitching error signature 1804 associated with the signal channelcannot be picked out of a spectrum like FIG. 18 b. Hence inadequacies inthe design of the coherent channel substitution system may be toleratedif the frequency hopping interval τ_(h) is sufficiently short.

2. Noise-Rendering

The information-bearing signal must be disguised to appear like opticalnoise. The inphase and quadrature parts of one SOP of an optical noisefield are each Gaussian noises. Optical noise contains power in bothpolarization states, although the optical noise could be purposelypolarized for this application. The distribution of the inphase part ofthe information-bearing signal depends on what modulation format isused, but it is typically not Gaussian. For example, if polarizationmultiplexed QAM is used with M_(s) bits/symbol, the x-polarization ofthe QAM signal takes on complex values u_(n) at the symbol centers (n=0,1, 2, . . . ), defined by the information to be transmitted. Thedistribution f(Re[u]) of the real part of u_(n) comprises 2^(M) ^(s)^(/4) delta spikes separated by d. For the example of 16 level QAM,f(Re[u]) comprises four delta spikes.

Two ways are discussed below to convert this distribution into aGaussian distribution, that is to noise-render the signal. The datacarried by the signal must appear random. It may be precoded ifnecessary, for example by performing an exclusive or operation with apseudorandom sequence derived from the key.

The first noise-rendering method begins by adding to u_(n) apseudorandom complex variable w_(n), whose real and imaginary parts eachfollow a uniform distribution

$\begin{matrix}{{f\left( {{Re}\lbrack w\rbrack} \right)} = \frac{1}{d}} & {{- \frac{d}{2}} \leq {{Re}\lbrack w\rbrack} \leq \frac{d}{2}} \\{{f\left( {{Re}\lbrack w\rbrack} \right)} = 0} & {{{{Re}\lbrack w\rbrack}} > \frac{d}{2}} \\{{f\left( {{Im}\lbrack w\rbrack} \right)} = \frac{1}{d}} & {{- \frac{d}{2}} \leq {{Im}\lbrack w\rbrack} \leq \frac{d}{2}} \\{{f\left( {{Im}\lbrack w\rbrack} \right)} = 0} & {{{{Im}\lbrack w\rbrack}} > \frac{d}{2}}\end{matrix}$The distribution of w_(n) appears as a square on the complex plane.w_(n) may be obtained from a pseudorandom data sequence which isgenerated from the key. The real and imaginary parts of u_(n)+w_(n) eachhas a uniform distribution from −2^(M) ^(s) ^(/4−1) d to 2^(M) ^(s)^(/4−1) d. Then the sum is transformed into a quantity having a Gaussiandistribution by taking the inverse error function of each part. Theresult may be used for that inphase component of the electric fieldenvelope

${E_{outx}\left( {n\;\tau_{s}} \right)} = {{\sqrt{2}\sigma\;{{inverf}\left( \frac{{Re}\left\lbrack {u_{n} + w_{n}} \right\rbrack}{2^{{M_{s}/4} - 1}d} \right)}} + {{\mathbb{i}}\sqrt{2}\sigma\;{{inverf}\left( \frac{{Im}\left\lbrack {u_{n} + w_{n}} \right\rbrack}{2^{{M_{s}/4} - 1}d} \right)}}}$where σ is the standard deviation of a component of the optical noise towhich the signal is to be matched. The inverse error function may bestored in a look-up table. Applying this transformation causes a penaltycompared to using the modulation format unaltered, 3.4 dB in the case ofQPSK.

The second noise-rendering method is to multiply u_(n)+w_(n) by a phasefactor e^(iθ) ^(n) and a real function q(|u_(n)+w_(n)|), to giveq(|u_(n)+w_(n)|)e^(iθ) ^(n) (u_(n)+w_(n))  (9)θ_(n) is a pseudorandom number sequence derived from the secret key, andis uniformly distributed between 0 and π/2. The phase argument of e^(iθ)^(n) (u_(n)+w_(n)) is therefore uniformly distributed from −π to π. Thefunction q(|u_(n)+w_(n)|) is the correct function to translate thedistribution of |u_(n)+w_(n)| onto a Rayleigh distribution. Since thequantity of equation 9 has a Rayleigh distributed amplitude and uniformphase, it is distributed like Gaussian noise. The advantage of thesecond noise-rendering method is that it preserves the phase ofu_(n)+w_(n), which has application in the optical phase recoveryoperation.

There are other ways of making the QAM signal appear like Gaussiannoise, and there are noise-rendering methods for other classes ofmodulation format.

A component of the signal's electric field envelope cannot be made to betruly Gaussian by the methods above because the finite range of the D/Aconverters prohibits setting extreme values, while the Gaussiandistribution extends to infinity. If the actual distribution deviatestoo much from Gaussian the eavesdropper can use this property in a testto decide if the channel being observed is likely to be the data-bearingchannel, and so weakens the security of the overall encryption method.The output of the coherent channel substitution scheme may be made toresemble Gaussian noise more closely by passing it through a passiveoptical component which has multipath interference (MPI) longer than onesymbol length. Such a component may be made in a planar waveguide systemby splitting the signal into several paths of different lengths andrecombining them, or by using multiple birefringent elements insequence. The transfer function of this passive component must bereversed at the receiver, for example by the corresponding mathematicaloperation in the receiver's DSP. The transformation of the passivecomponent should be made to change suddenly at intervals, according to asequence derived from the key, otherwise if the eavesdropper correctlyguesses the transformation at one point in time he can use thatknowledge from then on, and the code is weakened.

3. Symbol Clock Recovery

The receiver must recover the symbol clock, the optical phase and, inthe case where depolarized optical noise is used over a fiber opticlink, the correct polarization transformation. These tasks are morechallenging after the signal is disguised as Gaussian noise.

With a standard modulation format, the signal either contains a pilottone of the symbol clock, or applying a non-linearity generates somesymbol clock content. This is no longer the case after noise-rendering.In fact, if it were possible to see clock content so easily it could beused by an eavesdropper as a test to identify which channel carries thetrue information-bearing signal.

The symbol clock may be sent from transmitter to receiver outside thesignal channel. A dedicated uncoded wavelength channel may be used.Alternatively, the whole broadband optical noise spectrum may bemodulated with a tone at the clock frequency, so that theinformation-bearing channel does not appear different from the otherchannels. These methods may also deliver the clock to an eavesdropper,so it is more secure to rely on the clock being recovered from thenoise-rendered signal.

Variations in the phase of the symbol clock are slow since very highfrequency stability radio frequency sources are available, and becausethe change in propagation delay of long fiber optic links is slow. Oncesymbol clock has been acquired, its slow changes may be tracked. Initialacquisition may be completed by sweeping the clock phase coarsely overthe full range and using a metric of signal quality such as bit errorrate, or whether the digital signal is recovered at all, to determinewhich clock phase value is closest to optimum. The clock phase may thenbe optimized using the BER as a metric.

The propagation delay of a fiber link, and hence the clock phase,changes when the laser is hopped in frequency. The amount of delaychange may be predicted exactly by knowing the chromatic dispersion ofthe link. This quantity may be measured at the start of communicationsby determining the symbol phase at several different opticalfrequencies.

4. Polarization Recovery

The polarization transformation between transmitter and receiver isdescribed by three degrees of freedom, corresponding to the polar andazimuthal angles on the Poincaré sphere representation of the principlestates of polarization and the rotation angle. It changes in a randomfashion slowly due to movement of an optical fiber or temperaturechanges, perhaps varying between a few 10 s of uncorrelated SOPs in 1second. Once the correct polarization transformation has been found anychanges may be tracked. The polarization transformation at any point intime will vary over the frequency hopping band, because of thepolarization mode dispersion (PMD) of the optical fiber. Furthermore,the change in polarization transformation going from one opticalfrequency to another will itself change randomly with time. An SOPreference may be provided by a polarized channel at a differentwavelength from the signal. However, the optical frequency of thereference channel should be swept across the band in order to take intoaccount the variation of the polarization transformation with opticalfrequency. Of course the frequency hopping sequence must be chosen toavoid a collision with the reference channel. Alternatively, thebroadband optical noise may be polarized at the transmitter, asexplained above, so that polarization recovery becomes trivial. Again,providing a polarization reference helps an eavesdropper as well as theintended recipient, and it is more secure to derive the polarizationtransformation from the noise-rendered signal.

The polarization transformation may be acquired by first sweeping thethree SOP degrees of freedom coarsely over the full range, using asignal quality metric such as BER or the quality of the recoveredoptical phase, discussed below, to find the best point. A fineadjustment may then be made to find the optimum polarizationtransformation. This process must be completed at several opticalfrequencies in the FH plan, so as to gain knowledge of how PMD changesthe polarization transformation over optical frequency. The FH plan mustrevisit all regions of the available optical spectrum sufficientlyfrequently to derive an update to the polarization transformation at alloptical frequencies.

5. Optical Phase Recovery

The optical phase is the hardest of the three quantities to obtain.Unless an expensive narrow linewidth laser is used, the phase noise ofthe laser varies on a shorter timescale than the symbol clock phase orthe polarization transformation. In addition, the latter two quantitiesdo not have to be reacquired after hopping to a new frequency, giventhat the chromatic dispersion and the effect of polarization modedispersion are known. Typically, when a laser tunes in an opticalfrequency, the phase after tuning is unknown, and a frequency error mayalso occur. The optical phase must be reacquired at the start of eachfrequency hopping interval.

The frequency offset between the signal centre frequency and thereceiver local oscillator is generally within a small range, specifiedby the design of the transmitter and receiver. The optical phase andfrequency may be acquired by a search of the frequency and phase spacelooking for the presence of a recognizable signal and a low BER. Thisapproach may be slow or require a high level of parallelism in the DSP.If the time taken to acquire is longer than the available buffer in theDSP then some data will be lost at each FH interval.

When the second noise-rendering transformation described above is usedit is possible to acquire the carrier phase and frequency by a morestandard faster method. The electric field of one SOP of thenoise-rendered signal, as seen at the receiver, after inverting theeffect of the MPI passive, isq(|u_(n)+w_(n)|)e^(iθ) ^(n) ^(+i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ) ^(s)^((t)−φ) ^(LO) ^((t)))(u_(n)+w_(n))(ω_(s)−ω_(LO))t+φ_(s)(t)−φ_(LO)(t) is the phase difference between thesignal and the LO and is not yet known. Dividing by the inverse ofq(|u_(n)+w_(n)|), which does not change the phase angle, and multiplyingby e^(−iθ) ^(n) , which is known to the receiver, givese^(i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ) ^(s) ^((t)−φ) ^(LO)^((t)))u_(n)+e^(i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ) ^(s) ^((t)−φ) ^(LO)^((t)))w_(n)  (10)Even though the w_(n) are known, e^(i(ω) ^(s) ^(−ω) ^(LO) ^((t+i(φ) ^(s)^((t)−φ) ^(LO) ^((t)))w_(n) appears random, and its presence in theexpression makes direct phase recovery difficult. Phase recovery ispossible by selecting only those symbols where |w_(n)| is small, so thatthe received value of equation 10 is close to e^(i(ω) ^(s) ^(−ω) ^(LO)^()t+i(φ) ^(s) ^((t)−φ) ^(LO) ^((t)))u_(n), and the standard phaseestimation method for that modulation format may be used. The phaseestimation algorithm may be modified to weight the points inverselyaccording to |w_(n)|. For some QAM cases, for example QPSK, the step ofdividing by the inverse of q(|u_(n)+w_(n)|) does not affect the phaserecovery operation, and that step may be omitted to make the operationsimpler. Because it effectively uses only a few of the incoming symbols,this version of phase estimation algorithm requires narrower linewidthsignal and LO lasers and have a longer acquisition time than applyingthe standard algorithm to a signal that has not been noise-rendered. Ifthere is a buffer store in the DSP that is longer than the acquisitiontime, then the recovered phase may be applied to the early symbols inthe frequency hop interval, and there will be no data loss. Aneavesdropper who does not know w_(n) and θ_(n) cannot use this method torecover the optical frequency and phase.

An additional benefit of using the second noise-rendering method andpart of the optical phase acquisition algorithm is that it may be usedwith the symbol phase and polarization transformation acquisitionroutines as a signal quality metric. When the symbol phase andpolarization transformation are close to correct, the quantity|e^(i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ) ^(s) ^((t)−φ) ^(LO)^((t)))u_(n)+e^(i(ω) ^(s) ^(−ω) ^(LO) ^()t+i(φ) ^(s) ^((t)−φ) ^(LO)^((t)))w_(n)|is close to any of a small number of values at times when |w_(n)| islow. The number of allowed values is the number of possible values of|u_(n)|, which depends on the modulation format; for QPSK there is onlyone allowed value. The spread of values of this quantity at times when|w_(n)| is low may be used as a signal quality metric.

The main issues with optical phase recovery are avoided if the signallaser in the transmitter (the add laser) and the local oscillator in thereceiver are referenced to lines in a frequency-stabilizedoctave-spanning optical comb. The transmit site and receive site mayeach hold a comb generator, and these will contain identical opticalfrequencies to one another given that they use the same radio frequencyreference. The signal laser output should be phase locked to the comb.It does not have to be the same optical frequency as one of the lines inthe comb, but it has to differ from a line by a fixed frequency and nophase noise. The receiver local oscillator does not have to be phaselocked to the octave-spanning comb, but its frequency and phase shouldbe compared to one of the lines in the comb and known by the DSP. Thereceiver DSP then knows the exact frequency and phase of the LO comparedto the signal, apart from a slowly varying contribution to the phasefrom the varying length of the fiber optic link with temperature. Thechromatic dispersion needs to be known accurately, as it causes a jumpin optical phase after a frequency hop. Given that it is phase locked toan absolute reference, the frequency hopping executed by the transmittermay then be considered to be coherent frequency hopping.

F. Appendix

1. Use of Complex Numbers to Describe Modulated Signals

Complex numbers are used to describe sine and cosine functions becausethis notation is a compact way of including the phase of the sine waveor cosine wave. For example the electric field is written in the formE(t)=Re└E _(s) e ^(iωt)  (A1)where E_(s) is a complex number. This may be expressed in terms of sinesand cosines asE(t)=Re[E _(s)] cos(ωt)−Im[E _(s)] sin(ωt)Or if complex E_(s) is written in terms of its magnitude and phaseE _(s) =|E _(s) |e ^(iθ) ^(s)then A1 becomesE(t)=|E _(s)|cos(ωt+θ _(s))The complex number notation is compact because the phase of the sinewave is stored in the phase of the complex number.

In the above discussion are equations similar tobeat term=Re└E _(s) E _(LO) *e ^(iωt┘)  (A2)E_(LO)* is the complex conjugate of E_(LO), meaning that everyoccurrence of i is replaced with −i, andE _(LO) *=|E _(LO) |e ^(−iθ) ^(LO)A2 may be rewritten asbeat term=|E _(s) ∥E _(LO)|cos(ωt+θ _(s)−θ_(LO))The appearance of E_(s)E_(LO)* in A2 means to take the phase differencebetween E_(s) and E_(LO).

The power of an optical wave is given by the magnitude squared of thecomplex electric field, and does not have a sinusoid time dependence. Soin the case of a field given by A1power=(E _(s) e ^(iωt))*(E _(s) e ^(iωt))=|E _(s)|²

2. Jones Vectors

The state of polarization of an optical signal may be described by aJones vector. This is a two element column vector. Each element is thecomplex envelope of the electric field, i.e., phase informationincluded. The top element is the component of the field in thex-direction (horizontal) and the bottom element in the y-direction(vertical). In fact x and y may be an arbitrary pair of orthogonaldirections. “Optics” by E. Hecht (Addison-Wesley, 4th ed., 2001) gives athorough account of Jones vectors.

Some Jones vectors of familiar states of polarization are listed below.

$\begin{matrix}\begin{pmatrix}1 \\0\end{pmatrix} & {horizontal} \\\begin{pmatrix}0 \\1\end{pmatrix} & {vertical} \\{\frac{1}{\sqrt{2}}\begin{pmatrix}1 \\1\end{pmatrix}} & {{linearly}\mspace{14mu}{polarized}\mspace{14mu}{at}{\mspace{11mu}\;}45^{{^\circ}}} \\{\frac{1}{\sqrt{2}}\begin{pmatrix}1 \\i\end{pmatrix}} & {circular}\end{matrix}$

A Jones unit vector {circumflex over (p)} has the property that{circumflex over (p)}·{circumflex over (p)}*=1If light polarized in SOP {circumflex over (p)}₁ passes through apolarizer oriented in direction {circumflex over (p)}₂, then themagnitude of the electric field is scaled by {circumflex over(p)}₁·{circumflex over (p)}₂*, and the direction of the electric fieldis changed to {circumflex over (p)}₂. In general 0≦|{circumflex over(p)}₁·{circumflex over (p)}₂*|≦1.

When polarized light is passed through a linear optical element, thetransformation of the SOP is described by premultiplying by a 2×2 matrixcalled the Jones matrix of the optical element.

While the present invention is described herein with reference toillustrative embodiments for particular applications, it should beunderstood that the invention is not limited thereto. Those havingordinary skill in the art and access to the teachings provided hereinwill recognize additional modifications, applications, and embodimentswithin the scope thereof and additional fields in which the presentinvention would be of significant utility.

Thus, the present invention has been described herein with reference toa particular embodiment for a particular application. Those havingordinary skill in the art and access to the present teachings willrecognize additional modifications, applications and embodiments withinthe scope thereof.

It is therefore intended by the appended claims to cover any and allsuch applications, modifications and embodiments within the scope of thepresent invention.

1. An optical communications system receiving an input optical signaland producing an output optical signal, said optical communicationssystem comprising: a combining means for receiving the input opticalsignal and an add optical signal, said combining means combining theinput optical signal and add optical signal such that the input opticalsignal and the add optical signal coherently interfere to form theoutput optical signal; wherein the light source of the add opticalsignal is not the light source for the input optical signal, and theoptical spectrum of the add optical signal has substantial magnitude atthose frequencies where the optical spectrum of the input optical signalhas substantial magnitude; at least one laser; at least one modulationsubsystem; at least one digital to analog (D/A) converter; and a digitalsignal processor; and wherein: the input optical signal contains atleast one input wavelength division multiplexed channel, the outputoptical signal having at least one output wavelength divisionmultiplexed channel; and light from said lasers is modulated by saidmodulation subsystems; said combining means combines the modulated lightfrom said modulation subsystems with one another and with the inputoptical signal; each of said modulation subsystems is adjusted by atleast one analog voltage, said analog voltage being produced by one ofsaid D/A converters; said D/A converters are controlled by said digitalsignal processor; and the optical phase of light from said lasers withrespect to one another is known by said digital signal processor and theoptical phase of said input wavelength division multiplexed channelscompared to light from said lasers is known by said digital signalprocessor; and the combining means sending the output optical signal;whereby said output optical signal contains information.
 2. The opticalcommunication system of claim 1 further comprising: at least one inputmonitor; and at least one input monitor splitter; and wherein: each ofsaid input monitor splitters has directed to it light which at leastpartially corresponds to the input optical signal and each of said inputmonitor splitters separates a portion of power of the light directed tosaid input monitor splitter to form at least one replica of the lightdirected to said input monitor splitter; said input monitors receive thereplicas; each of said input monitors includes sampled coherentdetection means and delivers data to said digital signal processor; andsaid digital signal processor knows the electric field envelopes of saidinput wavelength division multiplexed channels.
 3. The opticalcommunication system of claim 1 wherein: replicas of light from saidlaser are directed to a phase comparison unit comprising a phasecomparison unit combiner, a photodetector and an (analog to digital) A/Dconverter; and light from said lasers is combined by said phasecomparison unit combiner and delivered to said photodetector, saidphotodetector is electrically connected to said A/D converter, and saidA/D converter communicates with said digital signal processor; wherebythe optical phase of light from said lasers with respect to one anotheris known by said digital signal processor.
 4. The optical communicationsystem of claim 1 further comprising a plurality of output monitorswherein: each of said output monitors receives light which at leastpartially corresponds to the output optical signal and each of saidoutput monitors comprises sampled coherent detection means; whereby saiddigital signal processor knows a basic parameter of said lasers comparedto one another and compared to said input wavelength divisionmultiplexed channels.
 5. The optical communication system of claim 1further comprising an output monitor wherein: said output monitorreceives an output monitor optical signal which is the output opticalsignal or a replica of the output optical signal; said output monitorincludes a sampled coherent detection means; and said sampled coherentdetection employs local oscillator light and said local oscillator lighttunes in wavelength over a period of time; whereby said digital signalprocessor knows a basic parameter of said lasers compared to one anotherand compared to said input wavelength division multiplexed channels. 6.An optical communications system comprising: a plurality of lasers; aplurality of modulation subsystems; an optical combining means; aplurality of digital to analog (D/A) converters; and a digital signalprocessor; and wherein: each of said plurality of lasers is modulated byone of said plurality of modulation subsystems; each of said modulationsubsystems is adjusted by at least one analog voltage, said analogvoltage being produced by one of said D/A converters; said D/Aconverters are controlled by said digital signal processor; the opticalphase difference between light from said lasers is known by said digitalsignal processor and the states of polarization of light from saidlasers with respect to one another is known by said digital signalprocessor; and the optical combining means combines light from saidmodulation subsystems to form an output optical signal; whereby theoutput optical signal occupies a contiguous region of optical spectrumwider than the optical spectrum occupied by any one of said modulatedlasers, and the output optical signal contains information.
 7. Theoptical communication system of claim 6 further comprising a phasecomparison unit, wherein: the phase comparison unit is in communicationwith the digital signal processor; and the phase comparison unitreceives light from the lasers, and calculates the phases of the laserswith respect to one another.
 8. A method of producing an output opticalsignal from an input optical signal, said method comprising the step of:coherently interfering said input optical signal with an add opticalsignal, the light source for the add optical signal being a differentlight source to the light source for the input optical signal, and theoptical spectrum of the add optical signal having a substantiallysimilar shape to the optical spectrum of the input optical signal;whereby the output optical signal contains information; wherein when theinput optical signal contains at least one input wavelength divisionmultiplexed channel and the output optical signal contains at least oneoutput wavelength division multiplexed channel, further comprising thesteps of: modulating light from at least one laser by at least onemodulation subsystem; combining light from said modulated lasers to formthe add optical signal; and controlling said modulation subsystems by adigital signal processor, said digital signal processor knowing theoptical phase of light from said lasers with respect to one another andknowing the optical phase of said input wavelength division multiplexedchannels compared to light from said lasers.
 9. The method of producingan output optical signal of claim 8, further comprising the steps of:directing light from said lasers to a photodetector producing anelectrical photodetector output signal; digitizing said electricalphotodetector output signal into photodetector output data; andcommunicating said photodetector output data to said digital signalprocessor; whereby said digital signal processor knows the optical phaseof light from said lasers with respect to one another.
 10. A method ofproducing an output optical signal comprising the steps of: modulating afirst laser having a first wavelength by a first modulation subsystem toproduce a first add optical signal; modulating a second laser having asecond wavelength by a second modulation subsystem to produce a secondadd optical signal; controlling said first and second modulationsubsystems by a digital signal processor, said digital signal processorknowing the optical phase difference between light from said first andsecond lasers and the states of polarization of light from said firstand second lasers with respect to one another; and choosing theseparation between said first wavelength and said second wavelength sothat said output optical signal occupies a contiguous region of opticalspectrum wider than the optical spectrum occupied by either of the firstadd optical signal or the second add optical signal; whereby the outputoptical signal contains information.
 11. The method of producing anoutput optical signal of claim 10 further comprising the step ofcomparing the phase of the first and second lasers by sampled coherentdetection, and communicating said phase to said digital signalprocessor.